International Journal of Differential Equations
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The latest articles from Hindawi Publishing Corporation
© 2015 , Hindawi Publishing Corporation . All rights reserved.

An Inverse Spectral Problem for the Matrix SturmLiouville Operator with a BesselType Singularity
Tue, 19 May 2015 13:30:31 +0000
http://www.hindawi.com/journals/ijde/2015/647396/
The inverse problem by the Weyl matrix is studied for the matrix SturmLiouville equation on a finite interval with a Besseltype singularity in the end of the interval. We construct special fundamental systems of solutions for this equation and prove the uniqueness theorem of the inverse problem.
Natalia Bondarenko
Copyright © 2015 Natalia Bondarenko. All rights reserved.

A Stability Result for the Solutions of a Certain System of FourthOrder Delay Differential Equation
Thu, 02 Apr 2015 14:10:01 +0000
http://www.hindawi.com/journals/ijde/2015/618359/
The main purpose of this work is to give sufficient conditions for the uniform stability of the zero solution of a certain fourthorder vector delay differential equation of the following form: By constructing a Lyapunov functional, we obtained the result of stability.
A. M. A. AbouElEla, A. I. Sadek, A. M. Mahmoud, and R. O. A. Taie
Copyright © 2015 A. M. A. AbouElEla et al. 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
http://www.hindawi.com/journals/ijde/2015/325102/
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
http://www.hindawi.com/journals/ijde/2015/340715/
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,
powerlogarithmic, exotic, and complicated expansions. Here we develop 3D Power
Geometry and apply it for calculation powerelliptic expansions of solutions to an
ODE. Among them we select regular powerelliptic 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
http://www.hindawi.com/journals/ijde/2015/203715/
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
http://www.hindawi.com/journals/ijde/2015/138629/
We consider the nonlinear eigenvalue problem , , , , where is a cubiclike 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
http://www.hindawi.com/journals/ijde/2014/383254/
We investigate the large time behavior of the global weak entropy solutions to the symmetric KeyfitzKranzer 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
http://www.hindawi.com/journals/ijde/2014/245350/
The purpose of the present paper is to investigate the mixed DirichletNeumann boundary value problems for the anisotropic LaplaceBeltrami 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 LaxMilgram 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 TwoPoint Boundary Value Problem of Fractional Differential Equations at Resonance
Tue, 05 Aug 2014 12:30:02 +0000
http://www.hindawi.com/journals/ijde/2014/632434/
We establish the existence results for twopoint 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 InsectBorne Diseases
Thu, 24 Jul 2014 07:14:43 +0000
http://www.hindawi.com/journals/ijde/2014/187685/
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 insectborne
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 insectborne 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 NonBazilevič 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 NonBazilevič 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 twopoint 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 SecondOrder 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 secondorder nonlinear delay dynamic equation with damping on a time scale , , where , , and are positive right dense continuous (rdcontinuous) functions on . Our results improve and extend some results established by Zhang et al., 2011. Also, our results unify the oscillation of the secondorder nonlinear delay differential equation with damping and the secondorder 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 SalamonWeiss 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 UMDproperty 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 quasistationary solutions of a free boundary
problem which had been discussed by Bueno (2005). Using a simpler method we prove that the quasisteady 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 EvenOrder HalfLinear 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 halflinear 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 VolterraFredholm 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 VolterraFredholm neutral functional integrodifferential equations with infinite delay in Banach spaces. To obtain a priori bounds of solutions required in KrasnoselskiSchaefer 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 TwoPoint 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 twopoint 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 SchrödingerKdV 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 SchrödingerKdV 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 righthand 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 TimeDelays
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 timedelay and saturating actuators, which is further to reduce the conservatism of neutral system. Based on the model transformation and the delaydividing 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 delaydependent 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 EmdenFowler 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 AlHamouri and Ali Zein
Copyright © 2014 Ruba AlHamouri and Ali Zein. All rights reserved.

The Research of Periodic Solutions of TimeVarying 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 timevarying 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.