International Journal of Differential Equations

https://www.hindawi.com/journals/ijde/

List of Papers (Total 577)

Redistribution of Nodes with Two Constraints in Meshless Method of Line to Time-Dependent Partial Differential Equations

Meshless method of line is a powerful device to solve time-dependent partial differential equations. In integrating step, choosing a suitable set of points, such as adaptive nodes in spatial domain, can be useful, although in some cases this can cause ill-conditioning. In this paper, to produce smooth adaptive points in each step of the method, two constraints are enforced in...

Redistribution of Nodes with Two Constraints in Meshless Method of Line to Time-Dependent Partial Differential Equations

Meshless method of line is a powerful device to solve time-dependent partial differential equations. In integrating step, choosing a suitable set of points, such as adaptive nodes in spatial domain, can be useful, although in some cases this can cause ill-conditioning. In this paper, to produce smooth adaptive points in each step of the method, two constraints are enforced in...

Connections between Some Concepts of Polynomial Trichotomy for Noninvertible Evolution Operators in Banach Spaces

The present paper treats three concepts of nonuniform polynomial trichotomies for noninvertible evolution operators acting on Banach spaces. The connections between these concepts are established through numerous examples and counterexamples for systems defined on the Banach space of square-summable sequences.

Existence for Elliptic Equation Involving Decaying Cylindrical Potentials with Subcritical and Critical Exponent

We consider the existence of nontrivial solutions to elliptic equations with decaying cylindrical potentials and subcritical exponent. We will obtain a local minimizer by using Ekeland’s variational principle.

Existence for Elliptic Equation Involving Decaying Cylindrical Potentials with Subcritical and Critical Exponent

We consider the existence of nontrivial solutions to elliptic equations with decaying cylindrical potentials and subcritical exponent. We will obtain a local minimizer by using Ekeland’s variational principle.

On the Initial-Boundary-Value Problem for the Time-Fractional Diffusion Equation on the Real Positive Semiaxis

We consider the time-fractional derivative in the Caputo sense of order . Taking into account the asymptotic behavior and the existence of bounds for the Mainardi and the Wright function in , two different initial-boundary-value problems for the time-fractional diffusion equation on the real positive semiaxis are solved. Moreover, the limit when of the respective solutions is...

On the Initial-Boundary-Value Problem for the Time-Fractional Diffusion Equation on the Real Positive Semiaxis

We consider the time-fractional derivative in the Caputo sense of order . Taking into account the asymptotic behavior and the existence of bounds for the Mainardi and the Wright function in , two different initial-boundary-value problems for the time-fractional diffusion equation on the real positive semiaxis are solved. Moreover, the limit when of the respective solutions is...

Propagation of Water Waves over Uneven Bottom under the Effect of Surface Tension

We establish existence and uniqueness of solutions to the Cauchy problem associated with a new one-dimensional weakly-nonlinear, weakly-dispersive system which arises as an asymptotical approximation of the full potential theory equations for modelling propagation of small amplitude water waves on the surface of a shallow channel with variable depth, taking into account the...

Propagation of Water Waves over Uneven Bottom under the Effect of Surface Tension

We establish existence and uniqueness of solutions to the Cauchy problem associated with a new one-dimensional weakly-nonlinear, weakly-dispersive system which arises as an asymptotical approximation of the full potential theory equations for modelling propagation of small amplitude water waves on the surface of a shallow channel with variable depth, taking into account the...

On the Convergence of a Nonlinear Boundary-Value Problem in a Perforated Domain

We consider a family with respect to a small parameter of nonlinear boundary-value problems as well as the corresponding spectral problems in a domain perforated periodically along a part of the boundary. We prove the convergence of solution of the original problems to the solution of the respective homogenized problem in this domain.

Propagation of Water Waves over Uneven Bottom under the Effect of Surface Tension

We establish existence and uniqueness of solutions to the Cauchy problem associated with a new one-dimensional weakly-nonlinear, weakly-dispersive system which arises as an asymptotical approximation of the full potential theory equations for modelling propagation of small amplitude water waves on the surface of a shallow channel with variable depth, taking into account the...

Nonlinear Impulsive Differential Equations with Weighted Exponential or Ordinary Dichotomous Linear Part in a Banach Space

We consider nonlinear impulsive differential equations with ψ-exponential and ψ-ordinary dichotomous linear part in a Banach space. By the help of Banach’s fixed-point principle sufficient conditions are found for the existence of ψ-bounded solutions of these equations on and .

Mean-Square Asymptotically Almost Automorphic Solutions to Fractional Stochastic Relaxation Equations

Mild solutions generated by a -regularized family to fractional stochastic relaxation equations are studied. The main objective is to establish the existence and uniqueness of square-mean asymptotically almost automorphic mild solutions to linear and semilinear case of these equations. Under different hypotheses, some new theorems concerning the main objective are derived.

Mean-Square Asymptotically Almost Automorphic Solutions to Fractional Stochastic Relaxation Equations

Mild solutions generated by a -regularized family to fractional stochastic relaxation equations are studied. The main objective is to establish the existence and uniqueness of square-mean asymptotically almost automorphic mild solutions to linear and semilinear case of these equations. Under different hypotheses, some new theorems concerning the main objective are derived.

Numerical Solution of Riccati Equations by the Adomian and Asymptotic Decomposition Methods over Extended Domains

We combine the Adomian decomposition method (ADM) and Adomian’s asymptotic decomposition method (AADM) for solving Riccati equations. We investigate the approximate global solution by matching the near-field approximation derived from the Adomian decomposition method with the far-field approximation derived from Adomian’s asymptotic decomposition method for Riccati equations and...

Periodic Solutions of Some Polynomial Differential Systems in Dimension 3 via Averaging Theory

We provide sufficient conditions for the existence of periodic solutions of the polynomial third order differential system ,  ,  and  , where , , and are polynomials in the variables , , and of degree with being periodic functions, is a real number, and is a small parameter.

Stability, Boundedness, and Existence of Periodic Solutions to Certain Third-Order Delay Differential Equations with Multiple Deviating Arguments

The behaviour of solutions for certain third-order nonlinear differential equations with multiple deviating arguments is considered. By employing Lyapunov’s second method, a complete Lyapunov functional is constructed and used to establish sufficient conditions that guarantee existence of unique solutions that are periodic, uniformly asymptotically stable, and uniformly...

Dynamical Behavior of a System of Second-Order Nonlinear Difference Equations

This paper is concerned with local stability, oscillatory character of positive solutions to the system of the two nonlinear difference equations , , where , , , and , .

Dynamical Behavior of a System of Second-Order Nonlinear Difference Equations

This paper is concerned with local stability, oscillatory character of positive solutions to the system of the two nonlinear difference equations , , where , , , and , .

Dynamical Behavior of a System of Second-Order Nonlinear Difference Equations

This paper is concerned with local stability, oscillatory character of positive solutions to the system of the two nonlinear difference equations , , where , , , and , .

Self-Similar Blow-Up Solutions of the KPZ Equation

Self-similar blow-up solutions for the generalized deterministic KPZ equation with are considered. The asymptotic behavior of self-similar solutions is studied.

Self-Similar Blow-Up Solutions of the KPZ Equation

Self-similar blow-up solutions for the generalized deterministic KPZ equation with are considered. The asymptotic behavior of self-similar solutions is studied.

The Rate at Which the Energy of Solutions for a Class of -Laplacian Wave Equation Decays

We will investigate the decay estimate of the energy of the global solutions to the p-Laplacian wave equation with dissipation of the form under suitable assumptions on the positive function . For this end we use the multiplier method combined with nonlinear integral inequalities given by Martinez; the proof is based on the construction of a special weight function that depends...

On Certain Subclasses of Analytic Multivalent Functions Using Generalized Salagean Operator

We introduce and study two subclasses of multivalent functions denoted by and . Further, by using the method of differential subordination, certain inclusion relations between the two subclasses aforementioned are given. Moreover, several consequences of the main results are also discussed.

On Certain Subclasses of Analytic Multivalent Functions Using Generalized Salagean Operator

We introduce and study two subclasses of multivalent functions denoted by and . Further, by using the method of differential subordination, certain inclusion relations between the two subclasses aforementioned are given. Moreover, several consequences of the main results are also discussed.