Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. Capturing the Data Uncertainty Change in the Cocaine Consumption in Spain Using an Epidemiologically Based Model Wed, 30 Nov 2016 06:34:12 +0000 http://www.hindawi.com/journals/aaa/2016/1758459/ A probabilistic model is proposed to study the transmission dynamics of the cocaine consumption in Spain during the period of 1995–2011. Using the so-called probabilistic fitting technique, we study if the model is able to capture the data uncertainty coming from surveys. The proposed model is formulated through a nonlinear system of difference equations whose coefficients are treated as stochastic processes. A discussion regarding the usefulness and limitations of probabilistic fitting technique in order to capture the data uncertainty of the proposed model is presented. Christopher Anaya, Clara Burgos, Juan-Carlos Cortés, and Rafael-J. Villanueva Copyright © 2016 Christopher Anaya et al. All rights reserved. A Variational Approach to Perturbed Discrete Anisotropic Equations Sun, 20 Nov 2016 13:06:26 +0000 http://www.hindawi.com/journals/aaa/2016/5676138/ We continue the study of discrete anisotropic equations and we will provide new multiplicity results of the solutions for a discrete anisotropic equation. We investigate the existence of infinitely many solutions for a perturbed discrete anisotropic boundary value problem. The approach is based on variational methods and critical point theory. Amjad Salari, Giuseppe Caristi, David Barilla, and Alfio Puglisi Copyright © 2016 Amjad Salari et al. All rights reserved. Existence and Boundedness of Solutions for Nonlinear Volterra Difference Equations in Banach Spaces Sun, 20 Nov 2016 11:29:31 +0000 http://www.hindawi.com/journals/aaa/2016/1319049/ We consider a class of nonlinear discrete-time Volterra equations in Banach spaces. Estimates for the norm of operator-valued functions and the resolvents of quasi-nilpotent operators are used to find sufficient conditions that all solutions of such equations are elements of an appropriate Banach space. These estimates give us explicit boundedness conditions. The boundedness of solutions to Volterra equations with infinite delay is also investigated. Rigoberto Medina Copyright © 2016 Rigoberto Medina. All rights reserved. Integrodifferential Inequalities Arising in the Theory of Differential Equations Mon, 14 Nov 2016 13:16:59 +0000 http://www.hindawi.com/journals/aaa/2016/3520236/ The goal of this paper is to achieve some new results related to integrodifferential inequalities of one independent variable which can be applied as a study of qualitative and quantitative properties of solutions of some nonlinear integral equations. Zareen A. Khan Copyright © 2016 Zareen A. Khan. All rights reserved. Resolvent for Non-Self-Adjoint Differential Operator with Block-Triangular Operator Potential Sun, 13 Nov 2016 12:31:01 +0000 http://www.hindawi.com/journals/aaa/2016/2964817/ A resolvent for a non-self-adjoint differential operator with a block-triangular operator potential, increasing at infinity, is constructed. Sufficient conditions under which the spectrum is real and discrete are obtained. Aleksandr Mikhailovich Kholkin Copyright © 2016 Aleksandr Mikhailovich Kholkin. All rights reserved. Mathematical Modeling of Hidden Intimate Partner Violence in Spain: A Quantitative and Qualitative Approach Thu, 10 Nov 2016 07:49:06 +0000 http://www.hindawi.com/journals/aaa/2016/8372493/ The fact that women are abused by their male partner is something that happens worldwide in the 21st century. In numerous cases, abuse only becomes publicly known when a fatal event occurs and is beyond any possible remedy, that is, when men murder their female partner. Since 2003, 793 (September 4, 2015) women have been assassinated by their significant other or excouple in Spain. Only 7.2% of murdered women had reported their fear and previous intimate partner violence (IPV) to the police. Even when the number of female victims is comparable to the number of victims by terrorism, the Government has not assigned an equal amount of resources to diminish the magnitude of this hidden social problem. In this paper, a mathematical epidemiological model to forecast intimate partner violence in Spain is constructed. Both psychological and physical aggressor subpopulations are predicted and simulated. The model’s robustness versus uncertain parameters is studied by a sensitivity analysis. E. De la Poza, L. Jódar, and S. Barreda Copyright © 2016 E. De la Poza et al. All rights reserved. Fréchet Envelopes of Nonlocally Convex Variable Exponent Hörmander Spaces Wed, 09 Nov 2016 13:26:34 +0000 http://www.hindawi.com/journals/aaa/2016/1393496/ We show that the dual of the variable exponent Hörmander space is isomorphic to the Hörmander space (when the exponent satisfies the conditions , the Hardy-Littlewood maximal operator is bounded on for some and is an open set in ) and that the Fréchet envelope of is the space . Our proofs rely heavily on the properties of the Banach envelopes of the -Banach local spaces of and on the inequalities established in the extrapolation theorems in variable Lebesgue spaces of entire analytic functions obtained in a previous article. Other results for , , are also given (e.g., all quasi-Banach subspace of is isomorphic to a subspace of , or is not isomorphic to a complemented subspace of the Shapiro space ). Finally, some questions are proposed. Joaquín Motos, María Jesús Planells, and César F. Talavera Copyright © 2016 Joaquín Motos et al. All rights reserved. Completeness of Ordered Fields and a Trio of Classical Series Tests Sun, 06 Nov 2016 11:45:48 +0000 http://www.hindawi.com/journals/aaa/2016/6023273/ This article explores the fate of the infinite series tests of Dirichlet, Dedekind, and Abel in the context of an arbitrary ordered field. It is shown that each of these three tests characterizes the Dedekind completeness of an Archimedean ordered field; specifically, none of the three is valid in any proper subfield of . The argument hinges on a contractive-type property for sequences in Archimedean ordered fields that are bounded and strictly increasing. For an arbitrary ordered field, it turns out that each of the tests of Dirichlet and Dedekind is equivalent to the sequential completeness of the field. Robert Kantrowitz and Michael M. Neumann Copyright © 2016 Robert Kantrowitz and Michael M. Neumann. All rights reserved. The Approximate Solutions of Three-Dimensional Diffusion and Wave Equations within Local Fractional Derivative Operator Sun, 30 Oct 2016 10:59:11 +0000 http://www.hindawi.com/journals/aaa/2016/2913539/ We used the local fractional variational iteration transform method (LFVITM) coupled by the local fractional Laplace transform and variational iteration method to solve three-dimensional diffusion and wave equations with local fractional derivative operator. This method has Lagrange multiplier equal to minus one, which makes the calculations more easily. The obtained results show that the presented method is efficient and yields a solution in a closed form. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new method. Hassan Kamil Jassim Copyright © 2016 Hassan Kamil Jassim. All rights reserved. Quasi-Hyperbolicity and Delay Semigroups Thu, 27 Oct 2016 14:44:01 +0000 http://www.hindawi.com/journals/aaa/2016/1984874/ We study quasi-hyperbolicity of the delay semigroup associated with the equation , where is the history function and is the generator of a quasi-hyperbolic semigroup. We give conditions under which the associated solution semigroup of this equation generates a quasi-hyperbolic semigroup. Shard Rastogi and Sachi Srivastava Copyright © 2016 Shard Rastogi and Sachi Srivastava. All rights reserved. Global Existence of Weak Solutions to a Fractional Model in Magnetoelastic Interactions Mon, 24 Oct 2016 10:56:22 +0000 http://www.hindawi.com/journals/aaa/2016/9238948/ The paper deals with global existence of weak solutions to a one-dimensional mathematical model describing magnetoelastic interactions. The model is described by a fractional Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We prove global existence by using Faedo-Galerkin/penalty method. Some commutator estimates are used to prove the convergence of nonlinear terms. Idriss Ellahiani, EL-Hassan Essoufi, and Mouhcine Tilioua Copyright © 2016 Idriss Ellahiani et al. All rights reserved. A Note on First Passage Functionals for Lévy Processes with Jumps of Rational Laplace Transforms Mon, 24 Oct 2016 07:18:39 +0000 http://www.hindawi.com/journals/aaa/2016/5914657/ This paper investigates the two-sided first exit problem for a jump process having jumps with rational Laplace transform. The corresponding boundary value problem is solved to obtain an explicit formula for the first passage functional. Also, we derive the distribution of the first passage time to two-sided barriers and the value at the first passage time. Djilali Ait-Aoudia Copyright © 2016 Djilali Ait-Aoudia. All rights reserved. Approximating the Solution Stochastic Process of the Random Cauchy One-Dimensional Heat Model Wed, 19 Oct 2016 06:43:21 +0000 http://www.hindawi.com/journals/aaa/2016/5391368/ This paper deals with the numerical solution of the random Cauchy one-dimensional heat model. We propose a random finite difference numerical scheme to construct numerical approximations to the solution stochastic process. We establish sufficient conditions in order to guarantee the consistency and stability of the proposed random numerical scheme. The theoretical results are illustrated by means of an example where reliable approximations of the mean and standard deviation to the solution stochastic process are given. A. Navarro-Quiles, J.-V. Romero, M.-D. Roselló, and M. A. Sohaly Copyright © 2016 A. Navarro-Quiles et al. All rights reserved. Hyperplanes That Intersect Each Ray of a Cone Once and a Banach Space Counterexample Wed, 19 Oct 2016 06:36:08 +0000 http://www.hindawi.com/journals/aaa/2016/9623090/ Suppose is a cone contained in real vector space . When does contain a hyperplane that intersects each of the 0-rays in exactly once? We build on results found in Aliprantis, Tourky, and Klee Jr.’s work to give a partial answer to this question. We also present an example of a salient, closed Banach space cone for which there does not exist a hyperplane that intersects each 0-ray in exactly once. Chris McCarthy Copyright © 2016 Chris McCarthy. All rights reserved. Antinormal Weighted Composition Operators Mon, 10 Oct 2016 11:18:36 +0000 http://www.hindawi.com/journals/aaa/2016/5767426/ Let , where is set of all positive integers and is the counting measure whose -algebra is the power set of . In this paper, we obtain necessary and sufficient conditions for a weighted composition operator to be antinormal on the Hilbert space . We also determine a class of antinormal weighted composition operators on Hardy space . Dilip Kumar and Harish Chandra Copyright © 2016 Dilip Kumar and Harish Chandra. All rights reserved. Certain Properties of Some Families of Generalized Starlike Functions with respect to -Calculus Sun, 25 Sep 2016 09:46:43 +0000 http://www.hindawi.com/journals/aaa/2016/6180140/ By making use of the concept of -calculus, various types of generalized starlike functions of order were introduced and studied from different viewpoints. In this paper, we investigate the relation between various former types of -starlike functions of order . We also introduce and study a new subclass of -starlike functions of order . Moreover, we give some properties of those -starlike functions with negative coefficient including the radius of univalency and starlikeness. Some illustrative examples are provided to verify the theoretical results in case of negative coefficient functions class. Ben Wongsaijai and Nattakorn Sukantamala Copyright © 2016 Ben Wongsaijai and Nattakorn Sukantamala. All rights reserved. Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness Sun, 18 Sep 2016 10:55:15 +0000 http://www.hindawi.com/journals/aaa/2016/4567092/ We obtain characterizations of compactness for resolvent families of operators and as applications we study the existence of mild solutions to nonlocal Cauchy problems for fractional derivatives in Banach spaces. We discuss here simultaneously the Caputo and Riemann-Liouville fractional derivatives in the cases and Rodrigo Ponce Copyright © 2016 Rodrigo Ponce. All rights reserved. Generalized Jensen-Mercer Inequality for Functions with Nondecreasing Increments Sun, 18 Sep 2016 08:49:09 +0000 http://www.hindawi.com/journals/aaa/2016/5231476/ In the year 2003, McD Mercer established an interesting variation of Jensen’s inequality and later in 2009 Mercer’s result was generalized to higher dimensions by M. Niezgoda. Recently, Asif et al. has stated an integral version of Niezgoda’s result for convex functions. We further generalize Niezgoda’s integral result for functions with nondecreasing increments and give some refinements with applications. In the way, we generalize an important result, Jensen-Boas inequality, using functions with nondecreasing increments. These results would constitute a valuable addition to Jensen-type inequalities in the literature. Asif R. Khan and Sumayyah Saadi Copyright © 2016 Asif R. Khan and Sumayyah Saadi. All rights reserved. Existence and Uniqueness Results for a Smooth Model of Periodic Infectious Diseases Wed, 14 Sep 2016 11:59:08 +0000 http://www.hindawi.com/journals/aaa/2016/1708527/ We prove the existence of a curve (with respect to the scalar delay) of periodic positive solutions for a smooth model of Cooke-Kaplan’s integral equation by using the implicit function theorem under suitable conditions. We also show a situation in which any bounded solution with a sufficiently small delay is isolated, clearing an asymptotic stability result of Cooke and Kaplan. Guy Degla Copyright © 2016 Guy Degla. All rights reserved. Optimality Conditions for Nondifferentiable Multiobjective Semi-Infinite Programming Problems Wed, 07 Sep 2016 09:43:37 +0000 http://www.hindawi.com/journals/aaa/2016/5367190/ We have considered a multiobjective semi-infinite programming problem with a feasible set defined by inequality constraints. First we studied a Fritz-John type necessary condition. Then, we introduced two constraint qualifications and derive the weak and strong Karush-Kuhn-Tucker (KKT in brief) types necessary conditions for an efficient solution of the considered problem. Finally an extension of a Caristi-Ferrara-Stefanescu result for the ()-invexity is proved, and some sufficient conditions are presented under this weak assumption. All results are given in terms of Clark subdifferential. D. Barilla, G. Caristi, and A. Puglisi Copyright © 2016 D. Barilla et al. All rights reserved. Existence of Solutions for Some Nonlinear Problems with Boundary Value Conditions Thu, 01 Sep 2016 11:49:37 +0000 http://www.hindawi.com/journals/aaa/2016/5283263/ We study the existence of solutions for nonlinear boundary value problems , where denotes the boundary conditions on a compact interval , is a homeomorphism such that , and is a continuous function. All the contemplated boundary value problems are reduced to finding a fixed point for one operator defined on a space of functions, and Schauder fixed point theorem or Leray-Schauder degree is used. Dionicio Pastor Dallos Santos Copyright © 2016 Dionicio Pastor Dallos Santos. All rights reserved. On the Existence of Infinitely Many Solutions for Nonlocal Systems with Critical Exponents Wed, 31 Aug 2016 08:13:37 +0000 http://www.hindawi.com/journals/aaa/2016/7197542/ We study a class of semilinear nonlocal elliptic systems posed on settings without compact Sobolev embedding. By employing critical point theory and concentration estimates, we prove the existence of infinitely many solutions for values of the dimension , where provided M. Khiddi and R. Echarghaoui Copyright © 2016 M. Khiddi and R. Echarghaoui. All rights reserved. Variational Approaches to Characterize Weak Solutions for Some Problems of Mathematical Physics Equations Thu, 25 Aug 2016 16:54:58 +0000 http://www.hindawi.com/journals/aaa/2016/2071926/ This paper is aimed at providing three versions to solve and characterize weak solutions for Dirichlet problems involving the -Laplacian and the -pseudo-Laplacian. In this way generalized versions for some results which use Ekeland variational principle, critical points for nondifferentiable functionals, and Ghoussoub-Maurey linear principle have been proposed. Three sequences of generalized statements have been developed starting from the most abstract assertions until their applications in characterizing weak solutions for some mathematical physics problems involving the abovementioned operators. Irina Meghea Copyright © 2016 Irina Meghea. All rights reserved. Discrete Approaches to Continuous Boundary Value Problems: Existence and Convergence of Solutions Wed, 24 Aug 2016 18:04:37 +0000 http://www.hindawi.com/journals/aaa/2016/3910972/ We investigate two types of first-order, two-point boundary value problems (BVPs). Firstly, we study BVPs that involve nonlinear difference equations (the “discrete” BVP); and secondly, we study BVPs involving nonlinear ordinary differential equations (the “continuous” BVP). We formulate some sufficient conditions under which the discrete BVP will admit solutions. For this, our choice of methods involves a monotone iterative technique and the method of successive approximations (a.k.a. Picard iterations) in the absence of Lipschitz conditions. Our existence results for the discrete BVP are of a constructive nature and are of independent interest in their own right. We then turn our attention to applying our existence results for the discrete BVP to the continuous BVP. We form new existence results for solutions to the continuous BVP with our methods involving linear interpolation of the data from the discrete BVP, combined with a priori bounds and the convergence Arzela-Ascoli theorem. Thus, our use of discrete BVPs to yield results for the continuous BVP may be considered as a discrete approach to continuous BVPs. Douglas R. Anderson and Christopher C. Tisdell Copyright © 2016 Douglas R. Anderson and Christopher C. Tisdell. All rights reserved. Maximality Theorems on the Sum of Two Maximal Monotone Operators and Application to Variational Inequality Problems Thu, 11 Aug 2016 12:48:53 +0000 http://www.hindawi.com/journals/aaa/2016/7826475/ Let be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space . Let and be maximal monotone operators. The maximality of the sum of two maximal monotone operators has been an open problem for many years. In this paper, new maximality theorems are proved for under weaker sufficient conditions. These theorems improved the well-known maximality results of Rockafellar who used condition and Browder and Hess who used the quasiboundedness of and condition . In particular, the maximality of is proved provided that , where is a proper, convex, and lower semicontinuous function. Consequently, an existence theorem is proved addressing solvability of evolution type variational inequality problem for pseudomonotone perturbation of maximal monotone operator. Teffera M. Asfaw Copyright © 2016 Teffera M. Asfaw. All rights reserved. On Some Inequalities Involving Three or More Means Mon, 08 Aug 2016 11:39:58 +0000 http://www.hindawi.com/journals/aaa/2016/1249604/ We investigate some results about mean-inequalities involving a large number of bivariate means. As application, we derive a lot of inequalities between four or more means among the standard means known in the literature. Mustapha Raïssouli and Mohamed Chergui Copyright © 2016 Mustapha Raïssouli and Mohamed Chergui. All rights reserved. Studying Radiation and Reaction Effects on Unsteady MHD Non-Newtonian (Walter’s B) Fluid in Porous Medium Tue, 26 Jul 2016 13:43:39 +0000 http://www.hindawi.com/journals/aaa/2016/9262518/ This paper describes the studied effects of thermal radiation and chemical reaction on unsteady MHD non-Newtonian (obeying Walter’s B model) fluid in porous medium. The resulting problems are solved numerically. Graphical results for various interesting parameters are presented. Also the effects of the different parameters on the skin-friction and the heat fluxes are obtained and discussed numerically. Gamal M. Abdel-Rahman Rashed and Faiza M. N. El-fayez Copyright © 2016 Gamal M. Abdel-Rahman Rashed and Faiza M. N. El-fayez. All rights reserved. Existence of General Competitive Equilibria: A Variational Approach Mon, 20 Jun 2016 14:28:46 +0000 http://www.hindawi.com/journals/aaa/2016/4969253/ We study the existence of general competitive equilibria in economies with agents and goods in a finite number. We show that there exists a Walras competitive equilibrium in all ownership private economies such that, for all consumers, initial endowments do not contain free goods and utility functions are locally Lipschitz quasiconcave. The proof of the existence of competitive equilibria is based on variational methods by applying a theoretical existence result for Generalized Quasi Variational Inequalities. G. Anello and F. Rania Copyright © 2016 G. Anello and F. Rania. All rights reserved. Twist Periodic Solutions in the Relativistic Driven Harmonic Oscillator Mon, 13 Jun 2016 12:23:30 +0000 http://www.hindawi.com/journals/aaa/2016/6084082/ We study the one-dimensional forced harmonic oscillator with relativistic effects. Under some conditions of the parameters, the existence of a unique stable periodic solution is proved which is of twist type. The results depend on a Twist Theorem for nonlinear Hill’s equations which is established and proved here. Daniel Núñez and Andrés Rivera Copyright © 2016 Daniel Núñez and Andrés Rivera. All rights reserved. Existence of Solutions for a Robin Problem Involving the -Laplace Operator Mon, 13 Jun 2016 07:45:05 +0000 http://www.hindawi.com/journals/aaa/2016/2349172/ In this article we study the nonlinear Robin boundary-value problem , on . Using the variational method, under appropriate assumptions on , we obtain results on existence and multiplicity of solutions. Mostafa Allaoui Copyright © 2016 Mostafa Allaoui. All rights reserved.