International Journal of Differential Equations The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. On the Limit Cycles of a Class of Generalized Kukles Polynomial Differential Systems via Averaging Theory Sun, 15 Mar 2015 09:14:19 +0000 We apply the averaging theory of first and second order to a class of generalized Kukles polynomial differential systems to study the maximum number of limit cycles of these systems. Amar Makhlouf and Amor Menaceur Copyright © 2015 Amar Makhlouf and Amor Menaceur. All rights reserved. Power Geometry and Elliptic Expansions of Solutions to the Painlevé Equations Thu, 05 Feb 2015 10:07:07 +0000 We consider an ordinary differential equation (ODE) which can be written as a polynomial in variables and derivatives. Several types of asymptotic expansions of its solutions can be found by algorithms of 2D Power Geometry. They are power, power-logarithmic, exotic, and complicated expansions. Here we develop 3D Power Geometry and apply it for calculation power-elliptic expansions of solutions to an ODE. Among them we select regular power-elliptic expansions and give a survey of all such expansions in solutions of the Painlevé equations . Alexander D. Bruno Copyright © 2015 Alexander D. Bruno. All rights reserved. Nonlocal Boundary Value Problems for -Difference Equations and Inclusions Tue, 27 Jan 2015 11:53:23 +0000 We study boundary value problems for -difference equations and inclusions with nonlocal and integral boundary conditions which have different quantum numbers. Some new existence and uniqueness results are obtained by using fixed point theorems. Examples are given to illustrate the results. Sotiris K. Ntouyas and Jessada Tariboon Copyright © 2015 Sotiris K. Ntouyas and Jessada Tariboon. All rights reserved. Asymptotic Behavior of the Bifurcation Diagrams for Semilinear Problems with Application to Inverse Bifurcation Problems Tue, 06 Jan 2015 07:13:07 +0000 We consider the nonlinear eigenvalue problem ,  ,  ,  , where is a cubic-like nonlinear term and is a parameter. It is known by Korman et al. (2005) that, under the suitable conditions on , there exist exactly three bifurcation branches (), and these curves are parameterized by the maximum norm of the solution corresponding to . In this paper, we establish the precise global structures for (), which can be applied to the inverse bifurcation problems. The precise local structures for () are also discussed. Furthermore, we establish the asymptotic shape of the spike layer solution , which corresponds to , as . Tetsutaro Shibata Copyright © 2015 Tetsutaro Shibata. All rights reserved. Asymptotic Behavior of Global Entropy Solutions for Nonstrictly Hyperbolic Systems with Linear Damping Tue, 18 Nov 2014 06:30:56 +0000 We investigate the large time behavior of the global weak entropy solutions to the symmetric Keyfitz-Kranzer system with linear damping. It is proved that as the entropy solutions tend to zero in the norm. Richard Alexander De la Cruz Guerrero, Juan Carlos Juajibioy Otero, and Leonardo Rendon Copyright © 2014 Richard Alexander De la Cruz Guerrero et al. All rights reserved. Mixed Boundary Value Problem on Hypersurfaces Sun, 17 Aug 2014 12:45:26 +0000 The purpose of the present paper is to investigate the mixed Dirichlet-Neumann boundary value problems for the anisotropic Laplace-Beltrami equation on a smooth hypersurface with the boundary in . is an bounded measurable positive definite matrix function. The boundary is decomposed into two nonintersecting connected parts and on the Dirichlet boundary conditions are prescribed, while on the Neumann conditions. The unique solvability of the mixed BVP is proved, based upon the Green formulae and Lax-Milgram Lemma. Further, the existence of the fundamental solution to is proved, which is interpreted as the invertibility of this operator in the setting , where is a subspace of the Bessel potential space and consists of functions with mean value zero. R. DuDuchava, M. Tsaava, and T. Tsutsunava Copyright © 2014 R. DuDuchava et al. All rights reserved. Existence of Solutions for Two-Point Boundary Value Problem of Fractional Differential Equations at Resonance Tue, 05 Aug 2014 12:30:02 +0000 We establish the existence results for two-point boundary value problem of fractional differential equations at resonance by means of the coincidence degree theory. Furthermore, a result on the uniqueness of solution is obtained. We give an example to demonstrate our results. Lei Hu, Shuqin Zhang, and Ailing Shi Copyright © 2014 Lei Hu et al. All rights reserved. An Existence Theorem for a Nonlocal Global Pandemic Model for Insect-Borne Diseases Thu, 24 Jul 2014 07:14:43 +0000 We construct and analyze a nonlocal global pandemic model that comprises a system of two nonlocal integrodifferential equations (functional differential equations) and an ordinary differential equation. This model was constructed by considering a spherical coordinate transformation of a previously established epidemiology model that can be applied to insect-borne diseases, like yellow fever. This transformation amounts to a nonlocal boundary value problem on the unit sphere and therefore can be interpreted as a global pandemic model for insect-borne diseases. We ultimately show that a weak solution to the weak formulation of this model exists using a fixed point argument, which calls upon the construction of a weak formulation and the existence and uniqueness of an auxiliary problem. John R. Cannon and Daniel J. Galiffa Copyright © 2014 John R. Cannon and Daniel J. Galiffa. All rights reserved. On Certain Class of Non-Bazilevič Functions of Order Defined by a Differential Subordination Thu, 17 Jul 2014 11:27:14 +0000 We introduce a new subclass of Non-Bazilevič functions of order . Some subordination relations and inequality properties are discussed. The results obtained generalize the related work of some authors. In addition, some other new results are also obtained. A. G. Alamoush and M. Darus Copyright © 2014 A. G. Alamoush and M. Darus. All rights reserved. Solving Singular Boundary Value Problems by Optimal Homotopy Asymptotic Method Sun, 29 Jun 2014 10:56:04 +0000 In this paper, optimal homotopy asymptotic method (OHAM) for the semianalytic solutions of nonlinear singular two-point boundary value problems has been applied to several problems. The solutions obtained by OHAM have been compared with the solutions of another method named as modified adomain decomposition (MADM). For testing the success of OHAM, both of the techniques have been analyzed against the exact solutions in all problems. It is proved by this paper that solutions of OHAM converge rapidly to the exact solution and show most effectiveness as compared to MADM. S. Zuhra, S. Islam, M. Idrees, Rashid Nawaz, I. A. Shah, and H. Ullah Copyright © 2014 S. Zuhra et al. All rights reserved. Oscillation of Second-Order Nonlinear Delay Dynamic Equations with Damping on Time Scales Sun, 22 Jun 2014 13:08:21 +0000 We use the generalized Riccati transformation and the inequality technique to establish some new oscillation criteria for the second-order nonlinear delay dynamic equation with damping on a time scale , , where , , and are positive right dense continuous (rd-continuous) functions on . Our results improve and extend some results established by Zhang et al., 2011. Also, our results unify the oscillation of the second-order nonlinear delay differential equation with damping and the second-order nonlinear delay difference equation with damping. Finally, we give some examples to illustrate our main results. H. A. Agwa, Ahmed M. M. Khodier, and Heba A. Hassan Copyright © 2014 H. A. Agwa et al. All rights reserved. Existence of Mild and Classical Solutions for Nonlocal Impulsive Integrodifferential Equations in Banach Spaces with Measure of Noncompactness Thu, 19 Jun 2014 07:51:38 +0000 We study the existence of mild and classical solutions are proved for a class of impulsive integrodifferential equations with nonlocal conditions in Banach spaces. The main results are obtained by using measure of noncompactness and semigroup theory. An example is presented. K. Karthikeyan, A. Anguraj, K. Malar, and Juan J. Trujillo Copyright © 2014 K. Karthikeyan et al. All rights reserved. On the Complex Inversion Formula and Admissibility for a Class of Volterra Systems Sun, 01 Jun 2014 07:34:24 +0000 This paper studies Volterra integral evolution equations of convolution type from the point of view of complex inversion formula and the admissibility in the Salamon-Weiss sens. We first present results on the validity of the inverse formula of the Laplace transform for the resolvent families associated with scalar Volterra integral equations of convolution type in Banach spaces, which extends and improves the results in Hille and Philllips (1957) and Cioranescu and Lizama (2003, Lemma 5), respectively, including the stronger version for a class of scalar Volterra integrodifferential equations of convolution type on unconditional martingale differences UMD spaces, provided that the leading operator generates a -semigroup. Next, a necessary and sufficient condition for -admissibility of the system's control operator is given in terms of the UMD-property of its underlying control space for a wider class of Volterra integrodifferential equations when the leading operator is not necessarily a generator, which provides a generalization of a result known to hold for the standard Cauchy problem (Bounit et al., 2010, Proposition 3.2). Ahmed Fadili and Hamid Bounit Copyright © 2014 Ahmed Fadili and Hamid Bounit. All rights reserved. Stability of Solutions to a Free Boundary Problem for Tumor Growth Wed, 21 May 2014 11:30:25 +0000 We study the asymptotic behaviour of quasi-stationary solutions of a free boundary problem which had been discussed by Bueno (2005). Using a simpler method we prove that the quasi-steady solutions of the problem converge uniformly to the unique nontrivial steady solution. Shihe Xu Copyright © 2014 Shihe Xu. All rights reserved. On the Oscillation of Even-Order Half-Linear Functional Difference Equations with Damping Term Mon, 19 May 2014 12:14:44 +0000 We investigate the oscillatory behavior of solutions of the th order half-linear functional difference equations with damping term of the form , , where is even and , is a fixed real number. Our main results are obtained via employing the generalized Riccati transformation. We provide two examples to illustrate the effectiveness of the proposed results. Yaşar Bolat and Jehad Alzabut Copyright © 2014 Yaşar Bolat and Jehad Alzabut. All rights reserved. Existence of Solution via Integral Inequality of Volterra-Fredholm Neutral Functional Integrodifferential Equations with Infinite Delay Wed, 14 May 2014 09:29:22 +0000 In this work we study existence results for mixed Volterra-Fredholm neutral functional integrodifferential equations with infinite delay in Banach spaces. To obtain a priori bounds of solutions required in Krasnoselski-Schaefer type fixed point theorem, we have used an integral inequality established by B. G. Pachpatte. The variants for obtained results are given. An example is considered to illustrate the obtained results. Kishor D. Kucche and Machindra B. Dhakne Copyright © 2014 Kishor D. Kucche and Machindra B. Dhakne. All rights reserved. Multiple Positive Solutions for a Coupled System of -Laplacian Fractional Order Two-Point Boundary Value Problems Wed, 07 May 2014 14:15:34 +0000 This paper establishes the existence of at least three positive solutions for a coupled system of -Laplacian fractional order two-point boundary value problems, , , , , , , , , , , by applying five functionals fixed point theorem. K. R. Prasad and B. M. B. Krushna Copyright © 2014 K. R. Prasad and B. M. B. Krushna. All rights reserved. An Extension of the Optimal Homotopy Asymptotic Method to Coupled Schrödinger-KdV Equation Wed, 07 May 2014 08:00:19 +0000 We consider the approximate solution of the coupled Schrödinger-KdV equation by using the extended optimal homotopy asymptotic method (OHAM). We obtained the extended OHAM solution of the problem and compared with the exact, variational iteration method (VIM) and homotopy perturbation method (HPM) solutions. The obtained solution shows that extended OHAM is effective, simpler, easier, and explicit and gives a suitable way to control the convergence of the approximate solution. Hakeem Ullah, Saeed Islam, Muhammad Idrees, Mehreen Fiza, and Zahoor Ul Haq Copyright © 2014 Hakeem Ullah et al. All rights reserved. The Partial Averaging of Fuzzy Differential Inclusions on Finite Interval Sun, 04 May 2014 12:03:47 +0000 The substantiation of a possibility of application of partial averaging method on finite interval for differential inclusions with the fuzzy right-hand side with a small parameter is considered. Andrej V. Plotnikov and Tatyana A. Komleva Copyright © 2014 Andrej V. Plotnikov and Tatyana A. Komleva. All rights reserved. Existence Results for an Impulsive Neutral Fractional Integrodifferential Equation with Infinite Delay Sun, 04 May 2014 08:56:51 +0000 We consider an impulsive neutral fractional integrodifferential equation with infinite delay in an arbitrary Banach space . The existence of mild solution is established by using solution operator and Hausdorff measure of noncompactness. Alka Chadha and Dwijendra N. Pandey Copyright © 2014 Alka Chadha and Dwijendra N. Pandey. All rights reserved. Further Stability Analysis on Neutral Systems with Actuator Saturation and Time-Delays Sun, 04 May 2014 06:50:55 +0000 This paper is concerned with the asymptotic stability analysis for a class of neutral systems with time-delay and saturating actuators, which is further to reduce the conservatism of neutral system. Based on the model transformation and the delay-dividing approach, a new type of augmented Lyapunov functional is constructed, which has fully exploited the information on the lower bound of the delay. Then the delay-dependent conditions for asymptotic stability are derived by applying some integral inequalities and Lyapunov theory. Finally, numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature. Xinghua Liu Copyright © 2014 Xinghua Liu. All rights reserved. Qualitative Theory of Differential, Difference, and Dynamic Equations Mon, 28 Apr 2014 09:54:05 +0000 Tongxing Li, Tuncay Candan, and Ethiraju Thandapani Copyright © 2014 Tongxing Li et al. All rights reserved. A Discrete Model for HIV Infection with Distributed Delay Sun, 27 Apr 2014 10:10:01 +0000 We give a consistent discretization of a continuous model of HIV infection, with distributed time delays to express the lag between the times when the virus enters a cell and when the cell becomes infected. The global stability of the steady states of the model is determined and numerical simulations are presented to illustrate our theoretical results. Brahim EL Boukari, Khalid Hattaf, and Noura Yousfi Copyright © 2014 Brahim EL Boukari et al. All rights reserved. Normal Hyperbolicity and Continuity of Global Attractors for a Nonlocal Evolution Equations Thu, 24 Apr 2014 09:41:09 +0000 We show the normal hyperbolicity property for the equilibria of the evolution equation and using the normal hyperbolicity property we prove the continuity (upper semicontinuity and lower semicontinuity) of the global attractors of the flow generated by this equation, with respect to functional parameter . Severino Horácio da Silva, Jocirei Dias Ferreira, and Flank David Morais Bezerra Copyright © 2014 Severino Horácio da Silva et al. All rights reserved. Resonant Problems by Quasilinearization Tue, 22 Apr 2014 08:34:11 +0000 The Dirichlet resonant boundary value problems are considered. If the respective nonlinear equation can be reduced to a quasilinear one with a nonresonant linear part and both equations are equivalent in some domain and if solutions of the quasilinear problem are in , then the original problem has a solution. We say then that the original problem allows for quasilinearization. If quasilinearization is possible for essentially different linear parts, then the original problem has multiple solutions. We give conditions for Emden-Fowler type resonant boundary value problem solvability and consider examples. Nadezhda Sveikate Copyright © 2014 Nadezhda Sveikate. All rights reserved. Oscillation Criteria for Certain Even Order Neutral Delay Differential Equations Wed, 16 Apr 2014 12:34:18 +0000 We establish sufficient conditions for the oscillation of solutions of even order neutral type differential equations of the form . Ruba Al-Hamouri and Ali Zein Copyright © 2014 Ruba Al-Hamouri and Ali Zein. All rights reserved. The Research of Periodic Solutions of Time-Varying Differential Models Wed, 16 Apr 2014 06:24:39 +0000 We have studied the periodicity of solutions of some nonlinear time-varying differential models by using the theory of reflecting functions. We have established a new relationship between the linear differential system and the Riccati equations and applied the obtained results to discuss the behavior of periodic solutions of the Riccati equations. Wenjun Liu, Yingxin Pan, and Zhengxin Zhou Copyright © 2014 Wenjun Liu et al. All rights reserved. On Inequality Applicable to Partial Dynamic Equations Tue, 15 Apr 2014 06:59:55 +0000 The main objective of the paper is to study new integral inequality on time scales which is used for the study of some partial dynamic equations. Some applications of our results are also given. Deepak B. Pachpatte Copyright © 2014 Deepak B. Pachpatte. All rights reserved. Global and Blow-Up Solutions for Nonlinear Hyperbolic Equations with Initial-Boundary Conditions Sun, 13 Apr 2014 16:38:35 +0000 We consider an initial-boundary value problem to a nonlinear string equations with linear damping term. It is proved that under suitable conditions the solution is global in time and the solution with a negative initial energy blows up in finite time. Ülkü Dinlemez and Esra Aktaş Copyright © 2014 Ülkü Dinlemez and Esra Aktaş. All rights reserved. Linearization of a Matrix Riccati Equation Associated to an Optimal Control Problem Sun, 06 Apr 2014 13:07:15 +0000 The matrix Riccati equation that must be solved to obtain the solution to stochastic optimal control problems known as LQG homing is linearized for a class of processes. The results generalize a theorem proved by Whittle and the one-dimensional case already considered by the authors. A particular two-dimensional problem is solved explicitly. Foued Zitouni and Mario Lefebvre Copyright © 2014 Foued Zitouni and Mario Lefebvre. All rights reserved.