International Journal of Differential Equations http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . 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 http://www.hindawi.com/journals/ijde/2014/458090/ 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 http://www.hindawi.com/journals/ijde/2014/287480/ 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 http://www.hindawi.com/journals/ijde/2014/594376/ 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 http://www.hindawi.com/journals/ijde/2014/319250/ 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 http://www.hindawi.com/journals/ijde/2014/948597/ 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 http://www.hindawi.com/journals/ijde/2014/427547/ 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 http://www.hindawi.com/journals/ijde/2014/791631/ 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 http://www.hindawi.com/journals/ijde/2014/784956/ 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 http://www.hindawi.com/journals/ijde/2014/485647/ 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 http://www.hindawi.com/journals/ijde/2014/106934/ 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 http://www.hindawi.com/journals/ijde/2014/307941/ 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 http://www.hindawi.com/journals/ijde/2014/780636/ 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 http://www.hindawi.com/journals/ijde/2014/102653/ 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 http://www.hindawi.com/journals/ijde/2014/234174/ 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 http://www.hindawi.com/journals/ijde/2014/138094/ 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 http://www.hindawi.com/journals/ijde/2014/625271/ 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 http://www.hindawi.com/journals/ijde/2014/564914/ 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 http://www.hindawi.com/journals/ijde/2014/437278/ 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 http://www.hindawi.com/journals/ijde/2014/430951/ 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 http://www.hindawi.com/journals/ijde/2014/949860/ 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 http://www.hindawi.com/journals/ijde/2014/724837/ 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 http://www.hindawi.com/journals/ijde/2014/741390/ 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. On Some Iterative Methods with Memory and High Efficiency Index for Solving Nonlinear Equations Sun, 06 Apr 2014 13:06:41 +0000 http://www.hindawi.com/journals/ijde/2014/495357/ Based on iterative methods without memory of eighth-order convergence proposed by Thukral (2012), some iterative methods with memory and high efficiency index are presented. We show that the order of convergence is increased without any additional function evaluations. Numerical comparisons are made to show the performance of the presented methods. Tahereh Eftekhari Copyright © 2014 Tahereh Eftekhari. All rights reserved. Periodic Boundary Value Problems for First-Order Impulsive Functional Integrodifferential Equations with Integral-Jump Conditions Sun, 23 Mar 2014 07:32:01 +0000 http://www.hindawi.com/journals/ijde/2014/791240/ By developing a new comparison result and using the monotone iterative technique, we are able to obtain existence of minimal and maximal solutions of periodic boundary value problems for first-order impulsive functional integrodifferential equations with integral-jump conditions. An example is also given to illustrate our results. Chatthai Thaiprayoon, Decha Samana, and Jessada Tariboon Copyright © 2014 Chatthai Thaiprayoon et al. All rights reserved. Multiscale Splitting Method for the Boltzmann-Poisson Equation: Application to the Dynamics of Electrons Mon, 03 Mar 2014 11:40:10 +0000 http://www.hindawi.com/journals/ijde/2014/178625/ We present a model based on dynamics of electrons in a plasma using a simplified Boltzmann equation coupled with Poisson’s equation. The motivation arose from simulating active plasma resonance spectroscopy, which is used for plasma diagnostic techniques; see Braithwaite and Franklin (2009), Lapke et al. (2010), and Oberrath et al. (2011). Mathematically, we are interested in designing splitting methods for the model problem. While the full Boltzmann equation is delicate to solve, we decouple it into a transport and collision part, which are then solved in different ways. First we reduce it to a simplified transport-collision equation and start to analyse the abstract Cauchy problem using semigroup methods. Second, we pass to the coupled transport and collision model and apply the splitting ideas, resecting the different discretization schemes. The results are discussed first with numerical experiments and then we verify the underlying theoretical novelties. Jürgen Geiser Copyright © 2014 Jürgen Geiser. All rights reserved. Conjugacy of a Discrete Semidynamical System in a Neighbourhood of the Nontrivial Invariant Manifold Tue, 25 Feb 2014 11:14:08 +0000 http://www.hindawi.com/journals/ijde/2014/703868/ The conjugacy of a discrete semidynamical system and its partially decoupled discrete semidynamical system in a Banach space is proved in a neighbourhood of the nontrivial invariant manifold. Andrejs Reinfelds Copyright © 2014 Andrejs Reinfelds. All rights reserved. Existence and Regularity for Boundary Cauchy Problems with Infinite Delay Mon, 20 Jan 2014 00:00:00 +0000 http://www.hindawi.com/journals/ijde/2014/379698/ The aim of this work is to investigate a class of boundary Cauchy problems with infinite delay. We give some sufficient conditions ensuring the uniqueness, existence, and regularity of solutions. For illustration, we apply the result to an age dependent population equation, which covers some special cases considered in some recent papers. Jung-Chan Chang Copyright © 2014 Jung-Chan Chang. All rights reserved. Qualitative Analysis of Solutions of Nonlinear Delay Dynamic Equations Mon, 30 Dec 2013 11:40:20 +0000 http://www.hindawi.com/journals/ijde/2013/764389/ We use the fixed point theory to investigate the qualitative analysis of a nonlinear delay dynamic equation on an arbitrary time scales. We illustrate our results by applying them to various kind of time scales. Mehmet Ünal and Youssef N. Raffoul Copyright © 2013 Mehmet Ünal and Youssef N. Raffoul. All rights reserved. A New Technique of Laplace Variational Iteration Method for Solving Space-Time Fractional Telegraph Equations Sun, 22 Dec 2013 13:17:26 +0000 http://www.hindawi.com/journals/ijde/2013/256593/ In this paper, the exact solutions of space-time fractional telegraph equations are given in terms of Mittage-Leffler functions via a combination of Laplace transform and variational iteration method. New techniques are used to overcome the difficulties arising in identifying the general Lagrange multiplier. As a special case, the obtained solutions reduce to the solutions of standard telegraph equations of the integer orders. Fatima A. Alawad, Eltayeb A. Yousif, and Arbab I. Arbab Copyright © 2013 Fatima A. Alawad et al. All rights reserved. Global Positive Periodic Solutions of Generalized -Species Gilpin-Ayala Delayed Competition Systems with Impulses Tue, 26 Nov 2013 14:38:30 +0000 http://www.hindawi.com/journals/ijde/2013/617824/ We consider the following generalized -species Lotka-Volterra type and Gilpin-Ayala type competition systems with multiple delays and impulses: , , ; , , By applying the Krasnoselskii fixed-point theorem in a cone of Banach space, we derive some verifiable necessary and sufficient conditions for the existence of positive periodic solutions of the previously mentioned. As applications, some special cases of the previous system are examined and some earlier results are extended and improved. Zhenguo Luo, Liping Luo, Jianhua Huang, and Binxiang Dai Copyright © 2013 Zhenguo Luo et al. All rights reserved.