International Journal of Differential Equations

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

List of Papers (Total 577)

Multiplicity of Positive Solutions for Fractional Differential Equation with -Laplacian Boundary Value Problems

We investigate the existence of multiple positive solutions of fractional differential equations with -Laplacian operator , , , , where , , , , , is a fixed integer, and , by applying Leggett–Williams fixed point theorems and fixed point index theory.

Numerical Solution of First-Order Linear Differential Equations in Fuzzy Environment by Runge-Kutta-Fehlberg Method and Its Application

The numerical algorithm for solving “first-order linear differential equation in fuzzy environment” is discussed. A scheme, namely, “Runge-Kutta-Fehlberg method,” is described in detail for solving the said differential equation. The numerical solutions are compared with (i)-gH and (ii)-gH differential (exact solutions concepts) system. The method is also followed by complete...

Qualitative Behaviour of Solutions in Two Models of Thin Liquid Films

For the thin-film model of a viscous flow which originates from lubrication approximation and has a full nonlinear curvature term, we prove existence of nonnegative weak solutions. Depending on initial data, we show algebraic or exponential dissipation of an energy functional which implies dissipation of the solution arc length that is a well known property for a Hele-Shaw flow...

Qualitative Behaviour of Solutions in Two Models of Thin Liquid Films

For the thin-film model of a viscous flow which originates from lubrication approximation and has a full nonlinear curvature term, we prove existence of nonnegative weak solutions. Depending on initial data, we show algebraic or exponential dissipation of an energy functional which implies dissipation of the solution arc length that is a well known property for a Hele-Shaw flow...

On Fuzzy Improper Integral and Its Application for Fuzzy Partial Differential Equations

We establish some important results about improper fuzzy Riemann integrals; we prove some properties of fuzzy Laplace transforms, which we apply for solving some fuzzy linear partial differential equations of first order, under generalized Hukuhara differentiability.

On Fuzzy Improper Integral and Its Application for Fuzzy Partial Differential Equations

We establish some important results about improper fuzzy Riemann integrals; we prove some properties of fuzzy Laplace transforms, which we apply for solving some fuzzy linear partial differential equations of first order, under generalized Hukuhara differentiability.

Equivariant Hopf Bifurcation in a Time-Delayed Ring of Antigenic Variants

We consider an intrahost malaria model allowing for antigenic variation within a single species. The host’s immune response is compartmentalised into reactions to major and minor epitopes. We investigate the dynamics of the model, paying particular attention to bifurcation and stability of the uniform nonzero endemic equilibrium. We establish conditions for the existence of an...

A New Result Concerning the Solvability of a Class of General Systems of Variational Equations with Nonmonotone Operators: Applications to Dirichlet and Neumann Nonlinear Problems

A new result of solvability for a wide class of systems of variational equations depending on parameters and governed by nonmonotone operators is found in a Banach real and reflexive space with applications to Dirichlet and Neumann problems related to nonlinear elliptic systems.

A New Result Concerning the Solvability of a Class of General Systems of Variational Equations with Nonmonotone Operators: Applications to Dirichlet and Neumann Nonlinear Problems

A new result of solvability for a wide class of systems of variational equations depending on parameters and governed by nonmonotone operators is found in a Banach real and reflexive space with applications to Dirichlet and Neumann problems related to nonlinear elliptic systems.

A New Result Concerning the Solvability of a Class of General Systems of Variational Equations with Nonmonotone Operators: Applications to Dirichlet and Neumann Nonlinear Problems

A new result of solvability for a wide class of systems of variational equations depending on parameters and governed by nonmonotone operators is found in a Banach real and reflexive space with applications to Dirichlet and Neumann problems related to nonlinear elliptic systems.

Existence and Permanence in a Diffusive KiSS Model with Robust Numerical Simulations

We have given an extension to the study of Kierstead, Slobodkin, and Skellam (KiSS) model. We present the theoretical results based on the survival and permanence of the species. To guarantee the long-term existence and permanence, the patch size denoted as must be greater than the critical patch size . It was also observed that the reaction-diffusion problem can be split into...

Existence and Permanence in a Diffusive KiSS Model with Robust Numerical Simulations

We have given an extension to the study of Kierstead, Slobodkin, and Skellam (KiSS) model. We present the theoretical results based on the survival and permanence of the species. To guarantee the long-term existence and permanence, the patch size denoted as must be greater than the critical patch size . It was also observed that the reaction-diffusion problem can be split into...

Existence and Permanence in a Diffusive KiSS Model with Robust Numerical Simulations

We have given an extension to the study of Kierstead, Slobodkin, and Skellam (KiSS) model. We present the theoretical results based on the survival and permanence of the species. To guarantee the long-term existence and permanence, the patch size denoted as must be greater than the critical patch size . It was also observed that the reaction-diffusion problem can be split into...

Existence and Permanence in a Diffusive KiSS Model with Robust Numerical Simulations

We have given an extension to the study of Kierstead, Slobodkin, and Skellam (KiSS) model. We present the theoretical results based on the survival and permanence of the species. To guarantee the long-term existence and permanence, the patch size denoted as must be greater than the critical patch size . It was also observed that the reaction-diffusion problem can be split into...

On Stability of Basis Property of Root Vectors System of the Sturm-Liouville Operator with an Integral Perturbation of Conditions in Nonstrongly Regular Samarskii-Ionkin Type Problems

We study a question on stability and instability of basis property of system of eigenfunctions and associated functions of the double differentiation operator with an integral perturbation of Samarskii-Ionkin type boundary conditions.

On -Anisotropic Problems with Neumann Boundary Conditions

This work is devoted to the study of a general class of anisotropic problems involving -Laplace operator. Based on the variational method, we establish the existence of a nontrivial solution without Ambrosetti-Rabinowitz type conditions.

Existence and Iteration of Positive Solutions to Third-Order BVP for a Class of -Laplacian Dynamic Equations on Time Scales

We investigate the existence and iteration of positive solutions for the following third-order -Laplacian dynamic equations on time scales: where is -Laplacian operator; that is, , and By applying the monotone iterative technique and without the assumption of the existence of lower and upper solutions, we not only obtain the existence of positive solutions for the problem, but...

Existence and Iteration of Positive Solutions to Third-Order BVP for a Class of -Laplacian Dynamic Equations on Time Scales

We investigate the existence and iteration of positive solutions for the following third-order -Laplacian dynamic equations on time scales: where is -Laplacian operator; that is, , and By applying the monotone iterative technique and without the assumption of the existence of lower and upper solutions, we not only obtain the existence of positive solutions for the problem, but...

Entropy Solution for Doubly Nonlinear Elliptic Anisotropic Problems with Robin Boundary Conditions

We study in this paper nonlinear anisotropic problems with Robin boundary conditions. We prove, by using the technic of monotone operators in Banach spaces, the existence of a sequence of weak solutions of approximation problems associated with the anisotropic Robin boundary value problem. For the existence and uniqueness of entropy solutions, we prove that the sequence of weak...

Solving the Telegraph and Oscillatory Differential Equations by a Block Hybrid Trigonometrically Fitted Algorithm

We propose a block hybrid trigonometrically fitted (BHT) method, whose coefficients are functions of the frequency and the step-size for directly solving general second-order initial value problems (IVPs), including systems arising from the semidiscretization of hyperbolic Partial Differential Equations (PDEs), such as the Telegraph equation. The BHT is formulated from eight...

Optimal Control of the Ill-Posed Cauchy Elliptic Problem

We give a characterization of the control for ill-posed problems of oscillating solutions. More precisely, we study the control of Cauchy elliptic problems via a regularization approach which generates incomplete information. We obtain a singular optimality system characterizing the no-regret control for the Cauchy problem.

Optimal Control of the Ill-Posed Cauchy Elliptic Problem

We give a characterization of the control for ill-posed problems of oscillating solutions. More precisely, we study the control of Cauchy elliptic problems via a regularization approach which generates incomplete information. We obtain a singular optimality system characterizing the no-regret control for the Cauchy problem.

Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality

The objective of this work is to make the numerical analysis, through the finite element method with Lagrange’s triangles of type 1, of a continuous optimal control problem governed by an elliptic variational inequality where the control variable is the internal energy . The existence and uniqueness of this continuous optimal control problem and its associated state system were...

Bounds for Products of Zeros of Solutions to Nonhomogeneous ODE with Polynomial Coefficients

We consider the equation , where is a polynomial and is an entire function. Let be the zeros of a solution to that equation. Lower estimates for the products are derived. In particular, they give us a bound for the zero free domain. Applications of the obtained estimates to the counting function of the zeros of solutions are also discussed.

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...