Articles

Solutions to Fractional Differential Equations with Nonlocal Initial Condition in Banach Spaces

A new existence and uniqueness theorem is given for solutions to differential equations involving the Caputo fractional derivative with nonlocal initial condition in Banach spaces. An application is also given.

Authors: Zhi-Wei Lv, Jin Liang and Ti-Jun Xiao

Control of Oscillating Systems with a Single Delay

Systems are considered related to the control of processes described by oscillating second-order systems of differential equations with a single delay. An explicit representation of solutions with the aid of s...

Authors: J Diblík, DYa Khusainov, J Lukáčová and M Růžičková

On Type of Periodicity and Ergodicity to a Class of Fractional Order Differential Equations

We study several types of periodicity to a class of fractional order differential equations.

Authors: RaviP Agarwal, Brunode Andrade and Claudio Cuevas

On the Oscillation of Second-Order Neutral Delay Differential Equations

Some new oscillation criteria for the second-order neutral delay differential equation , ...

Authors: Zhenlai Han, Tongxing Li, Shurong Sun and Weisong Chen

Stability Results for a Class of Difference Systems with Delay

Considering the linear delay difference system , where ,

Authors: Eva Kaslik

Permanence and Stable Periodic Solution for a Discrete Competitive System with Multidelays

The permanence and the existence of periodic solution for a discrete nonautonomous competitive system with multidelays are considered. Also the stability of the periodic solution is discussed. Numerical exampl...

Authors: Chunqing Wu

Boundary Controllability of Nonlinear Fractional Integrodifferential Systems

Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an a...

Authors: Hamdy M. Ahmed

Complete Asymptotic Analysis of a Nonlinear Recurrence Relation with Threshold Control

We consider a three-term nonlinear recurrence relation involving a nonlinear filtering function with a positive threshold . We work out ...

Authors: Qi Ge, Chengmin Hou and SuiSun Cheng

Oscillation Behavior of Third-Order Neutral Emden-Fowler Delay Dynamic Equations on Time Scales

We will establish some oscillation criteria for the third-order Emden-Fowler neutral delay dynamic equations on a time scale

Authors: Zhenlai Han, Tongxing Li, Shurong Sun and Chenghui Zhang

Stability of an Additive-Cubic-Quartic Functional Equation

In this paper, we consider the additive-cubic-quartic functional equation and prove the generalized Hyers-Ulam stability of the additiv...

Authors: M. Eshaghi-Gordji, S. Kaboli-Gharetapeh, Choonkil Park and Somayyeh Zolfaghari

Existence of Positive Solutions to a Nonlocal Boundary Value Problem with -Laplacian onTime Scales

The nonlocal boundary value problem, with -Laplacian of the form

Authors: Ting-Ting Sun, Lin-Lin Wang and Yong-Hong Fan

Existence of Positive Periodic Solutions to -Species Nonautonomous Food Chains with Harvesting Terms

By using Mawhin's continuation theorem of coincidence degree theory and some skills of inequalities, we establish the existence of at least

Authors: Yongkun Li and Kaihong Zhao

Nonlinear Discrete Periodic Boundary Value Problems at Resonance

Let be an integer with , and let ...

Authors: Ruyun Ma and Huili Ma

A Note on a Semilinear Fractional Differential Equation of Neutral Type with Infinite Delay

We deal in this paper with the mild solution for the semilinear fractional differential equation of neutral type with infinite delay: ,

Authors: Gisle M. Mophou and Gaston M. N'Guérékata

Pairs of Function Spaces and Exponential Dichotomy on the Real Line

We provide a complete diagram of the relation between the admissibility of pairs of Banach function spaces and the exponential dichotomy of evolution families on the real line. We prove that if

Authors: Adina Luminiţa Sasu

Mild Solutions for Fractional Differential Equations with Nonlocal Conditions

This paper is concerned with the existence and uniqueness of mild solution of the fractional differential equations with nonlocal conditions

Authors: Fang Li

Global Dynamics of a Competitive System of Rational Difference Equations in the Plane

We investigate global dynamics of the following systems of difference equations , ...

Authors: S. Kalabušić, M. R. S. Kulenović and E. Pilav

Nonlinear Delay Discrete Inequalities and Their Applications to Volterra Type Difference Equations

Delay discrete inequalities with more than one nonlinear term are discussed, which generalize some known results and can be used in the analysis of various problems in the theory of certain classes of discrete...

Authors: Yu Wu, Xiaopei Li and Shengfu Deng

A Delayed Chemostat Model with Impulsive Diffusion and Input on Nutrients

A chemostat model with delayed response in growth and impulsive diffusion and input on nutrients is considered. Using the discrete dynamical system determined by the stroboscopic map, we obtain a microorganism...

Authors: Jianjun Jiao and Shaohong Cai

Banded Matrices and Discrete Sturm-Liouville Eigenvalue Problems

We consider eigenvalue problems for self-adjoint Sturm-Liouville difference equations of any even order. It is well known that such problems with Dirichlet boundary conditions can be transformed into an algebraic...

Authors: Werner Kratz

Boundary Value Problems on Time Scales

Authors: Alberto Cabada and Victoria Otero-Espinar

Three Positive Periodic Solutions for a Class of Higher-Dimensional Functional Differential Equations with Impulses on Time Scales

By using a multiple fixed point theorem (Avery-Peterson fixed point theorem) for cones, some criteria are established for the existence of three positive periodic solutions for a class of higher-dimensional fu...

Authors: Yongkun Li and Meng Hu

Vartiational Optimal-Control Problems with Delayed Arguments on Time Scales

This paper deals with variational optimal-control problems on time scales in the presence of delay in the state variables. The problem is considered on a time scale unifying the discrete, the continuous, and t...

Authors: Thabet Abdeljawad (Maraaba), Fahd Jarad and Dumitru Baleanu

Doubly Periodic Traveling Waves in a Cellular Neural Network with Linear Reaction

Szekeley observed that the dynamic pattern of the locomotion of salamanders can be explained by periodic vector sequences generated by logical neural networks. Such sequences can mathematically be described by...

Authors: JianJhong Lin and SuiSun Cheng

Existence of Periodic Solutions for -Laplacian Equations on Time Scales

We systematically explore the periodicity of Liénard type -Laplacian equations on time scales. Sufficient criteria are established for t...

Authors: Fengjuan Cao, Zhenlai Han and Shurong Sun

On Connection between Second-Order Delay Differential Equations and Integrodifferential Equations with Delay

The existence and uniqueness of solutions and a representation of solution formulas are studied for the following initial value problem:

Authors: Leonid Berezansky, Josef Diblík and Zdenĕk Šmarda

On the Superstability Related with the Trigonometric Functional Equation

We will investigate the superstability of the (hyperbolic) trigonometric functional equation from the following functional equations: ,

Authors: Gwang Hui Kim

Asymptotic Behavior of Equilibrium Point for a Class of Nonlinear Difference Equation

We study the asymptotic behavior of the solutions for the following nonlinear difference equation where the initial conditions

Authors: Chang-you Wang, Fei Gong, Shu Wang, Lin-rui Li and Qi-hong Shi

Multiple Positive Solutions of -Point BVPs for Third-Order -Laplacian Dynamic Equations on Time Scales

This paper is concerned with the existence of multiple positive solutions for the third-order -Laplacian dynamic equation

Authors: Li-Hua Bian, Xi-Ping He and Hong-Rui Sun

The Existence of Periodic Solutions for Non-Autonomous Differential Delay Equations via Minimax Methods

By using variational methods directly, we establish the existence of periodic solutions for a class of nonautonomous differential delay equations which are superlinear both at zero and at infinity.

Authors: Rong Cheng

Solutions of 2 th-Order Boundary Value Problem for Difference Equation via Variational Method

The variational method and critical point theory are employed to investigate the existence of solutions for 2 th-order difference equatio...

Authors: Qingrong Zou and Peixuan Weng

On the Nonexistence and Existence of Solutions for a Fourth-Order Discrete Boundary Value Problem

By using the critical point theory, we establish various sets of sufficient conditions on the nonexistence and existence of solutions for the boundary value problems of a class of fourth-order difference equat...

Authors: Shenghuai Huang and Zhan Zhou

Necessary and Sufficient Conditions for the Existence of Positive Solution for Singular Boundary Value Problems on Time Scales

By constructing available upper and lower solutions and combining the Schauder's fixed point theorem with maximum principle, this paper establishes sufficient and necessary conditions to guarantee the existenc...

Authors: Meiqiang Feng, Xuemei Zhang, Xianggui Li and Weigao Ge

Dynamics for Nonlinear Difference Equation

We mainly study the global behavior of the nonlinear difference equation in the title, that is, the global asymptotical stability of zero equilibrium, the existence of unbounded solutions, the existence of per...

Authors: Dongmei Chen, Xianyi Li and Yanqin Wang

Some Basic Difference Equations of Schrödinger Boundary Value Problems

We consider special basic difference equations which are related to discretizations of Schrödinger equations on time scales with special symmetry properties, namely, so-called basic discrete grids. These grids...

Authors: Andreas Ruffing, Maria Meiler and Andrea Bruder

Existence of Nonoscillatory Solutions to Second-Order Neutral Delay Dynamic Equations on Time Scales

We employ Kranoselskii's fixed point theorem to establish the existence of nonoscillatory solutions to the second-order neutral delay dynamic equation

Authors: Tongxing Li, Zhenlai Han, Shurong Sun and Dianwu Yang

Summation Characterization of the Recessive Solution for Half-Linear Difference Equations

We show that the recessive solution of the second-order half-linear difference equation ,   ...

Authors: Ondřej Došlý and Simona Fišnarová

Dynamic Analysis of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Delays

Stochastic effects on convergence dynamics of reaction-diffusion Cohen-Grossberg neural networks (CGNNs) with delays are studied. By utilizing Poincaré inequality, constructing suitable Lyapunov functionals, a...

Authors: Jie Pan and Shouming Zhong

On the Recursive Sequence

In this paper we study the boundedness, the persistence, the attractivity and the stability of the positive solutions of the nonlinear difference equation ...

Authors: C. J. Schinas, G. Papaschinopoulos and G. Stefanidou

A Functional Inequality in Restricted Domains of Banach Modules

We investigate the stability problem for the following functional inequality on restricted domains of Banach modules over a

Authors: M. B. Moghimi, Abbas Najati and Choonkil Park

A Global Description of the Positive Solutions of Sublinear Second-Order Discrete Boundary Value Problems

Let be an integer with , ...

Authors: Ruyun Ma, Youji Xu and Chenghua Gao

Permanence of a Discrete -Species Schoener Competition System with Time Delays and Feedback Controls

A discrete -species Schoener competition system with time delays and feedback controls is proposed. By applying the comparison theorem o...

Authors: Xuepeng Li and Wensheng Yang

Nonlocal Controllability for the Semilinear Fuzzy Integrodifferential Equations in -Dimensional Fuzzy Vector Space

We study the existence and uniqueness of solutions and controllability for the semilinear fuzzy integrodifferential equations in -dimens...

Authors: YoungChel Kwun, JeongSoon Kim, MinJi Park and JinHan Park

Symmetry Properties of Higher-Order Bernoulli Polynomials

We investigate properties of identities and some interesting identities of symmetry for the Bernoulli polynomials of higher order using the multivariate

Authors: Taekyun Kim, Kyung-Won Hwang and Young-Hee Kim

Results and Conjectures about Order Lyness' Difference Equation in , with a Particular Study of the Case

We study order Lyness' difference equation in , with

Authors: G. Bastien and M. Rogalski

Asymptotic Behavior of Impulsive Infinite Delay Difference Equations with Continuous Variables

A class of impulsive infinite delay difference equations with continuous variables is considered. By establishing an infinite delay difference inequality with impulsive initial conditions and using the propert...

Authors: Zhixia Ma and Liguang Xu

Stability of a Generalized Euler-Lagrange Type Additive Mapping and Homomorphisms in -Algebras

Let be Banach modules over a -algebra and let

Authors: Abbas Najati and Choonkil Park

A Fixed Point Approach to the Stability of a Quadratic Functional Equation in -Algebras

We use a fixed point method to investigate the stability problem of the quadratic functional equation in ...

Authors: Mohammad B. Moghimi, Abbas Najati and Choonkil Park

Existence of Solutions for Nonlinear Four-Point -Laplacian Boundary Value Problems on Time Scales

We are concerned with proving the existence of positive solutions of a nonlinear second-order four-point boundary value problem with a -...

Authors: S. Gulsan Topal, O. Batit Ozen and Erbil Cetin

Global Behavior of Solutions to Two Classes of Second-Order Rational Difference Equations

For nonnegative real numbers , , ...

Authors: Sukanya Basu and Orlando Merino