Boundary Value Problems

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List of Papers (Total 1,603)

Nontrivial solutions of second-order singular Dirichlet systems

We study the existence of nontrivial solutions for second-order singular Dirichlet systems. The proof is based on a well-known fixed point theorem in cones and the Leray-Schauder nonlinear alternative principle. We consider a very general singularity and generalize some recent results.

Existence of positive solutions for a fractional elliptic problems with the Hardy-Sobolev-Maz’ya potential and critical nonlinearities

In this paper, we consider the study of a fractional elliptic problem with the Hardy-Sobolev-Maz’ya potential and critical nonlinearities. By means of variational methods and suitable technique, a positive solution to this problem is obtained.

Boundary value problems for strongly nonlinear equations under a Wintner-Nagumo growth condition

We study the following strongly nonlinear differential equation: ( a ( t , x ( t ) ) Φ ( x ′ ( t ) ) ) ′ = f ( t , x ( t ) , x ′ ( t ) ) , a.e. in  [ 0 , T ] $$\bigl(a \bigl(t,x(t) \bigr)\Phi\bigl(x'(t) \bigr) \bigr)

New approximation methods for solving elliptic boundary value problems via Picard-Mann iterative processes with mixed errors

In this paper, we introduce and study a class of new Picard-Mann iterative methods with mixed errors for common fixed points of two different nonexpansive and contraction operators. We also give convergence and stability analysis of the new Picard-Mann iterative approximation and propose numerical examples to show that the new Picard-Mann iteration converges more effectively than...

Nontrivial solutions of second-order singular Dirichlet systems

We study the existence of nontrivial solutions for second-order singular Dirichlet systems. The proof is based on a well-known fixed point theorem in cones and the Leray-Schauder nonlinear alternative principle. We consider a very general singularity and generalize some recent results.

Existence of positive solutions for a fractional elliptic problems with the Hardy-Sobolev-Maz’ya potential and critical nonlinearities

In this paper, we consider the study of a fractional elliptic problem with the Hardy-Sobolev-Maz’ya potential and critical nonlinearities. By means of variational methods and suitable technique, a positive solution to this problem is obtained.

A natural boundary element method for the Sobolev equation in the 2D unbounded domain

In this article, we devote ourselves to establishing a natural boundary element (NBE) method for the Sobolev equation in the 2D unbounded domain. To this end, we first constitute the time semi-discretized super-convergence format for the Sobolev equation by means of the Newmark method. Then, using the principle of natural boundary reduction, we establish a fully discretized NBE...

Nontrivial solutions of second-order singular Dirichlet systems

We study the existence of nontrivial solutions for second-order singular Dirichlet systems. The proof is based on a well-known fixed point theorem in cones and the Leray-Schauder nonlinear alternative principle. We consider a very general singularity and generalize some recent results.

Existence of positive solutions for a fractional elliptic problems with the Hardy-Sobolev-Maz’ya potential and critical nonlinearities

In this paper, we consider the study of a fractional elliptic problem with the Hardy-Sobolev-Maz’ya potential and critical nonlinearities. By means of variational methods and suitable technique, a positive solution to this problem is obtained.

On the Wiener criterion in higher dimensions

The Wiener criterion is a sufficient and necessary condition for the solvability of the Dirichlet problem. However, its geometric interpretation is not clear. In the case that the domain satisfies an exterior spine condition, the requirement for the spine is clear in dimension 3. In this note, we intend to obtain the condition that the exterior spine should satisfy in higher...

A natural boundary element method for the Sobolev equation in the 2D unbounded domain

In this article, we devote ourselves to establishing a natural boundary element (NBE) method for the Sobolev equation in the 2D unbounded domain. To this end, we first constitute the time semi-discretized super-convergence format for the Sobolev equation by means of the Newmark method. Then, using the principle of natural boundary reduction, we establish a fully discretized NBE...

Nontrivial solutions of second-order singular Dirichlet systems

We study the existence of nontrivial solutions for second-order singular Dirichlet systems. The proof is based on a well-known fixed point theorem in cones and the Leray-Schauder nonlinear alternative principle. We consider a very general singularity and generalize some recent results.

On the Wiener criterion in higher dimensions

The Wiener criterion is a sufficient and necessary condition for the solvability of the Dirichlet problem. However, its geometric interpretation is not clear. In the case that the domain satisfies an exterior spine condition, the requirement for the spine is clear in dimension 3. In this note, we intend to obtain the condition that the exterior spine should satisfy in higher...

A natural boundary element method for the Sobolev equation in the 2D unbounded domain

In this article, we devote ourselves to establishing a natural boundary element (NBE) method for the Sobolev equation in the 2D unbounded domain. To this end, we first constitute the time semi-discretized super-convergence format for the Sobolev equation by means of the Newmark method. Then, using the principle of natural boundary reduction, we establish a fully discretized NBE...

Nontrivial solutions of second-order singular Dirichlet systems

We study the existence of nontrivial solutions for second-order singular Dirichlet systems. The proof is based on a well-known fixed point theorem in cones and the Leray-Schauder nonlinear alternative principle. We consider a very general singularity and generalize some recent results.

On the Wiener criterion in higher dimensions

The Wiener criterion is a sufficient and necessary condition for the solvability of the Dirichlet problem. However, its geometric interpretation is not clear. In the case that the domain satisfies an exterior spine condition, the requirement for the spine is clear in dimension 3. In this note, we intend to obtain the condition that the exterior spine should satisfy in higher...

Fractional-order differential equations with anti-periodic boundary conditions: a survey

We will present an up-to-date review on anti-periodic boundary value problems of fractional-order differential equations and inclusions. Some recent and new results on nonlinear coupled fractional differential equations supplemented with coupled anti-periodic boundary conditions will also be highlighted.

Steady compressible heat-conductive fluid with inflow boundary condition

In this paper, we study strong solutions to the steady compressible heat-conductive fluid near a non-zero constant flow with the Dirichlet boundary condition for the velocity on the inflow and outflow part of the boundary. We also consider the Dirichlet boundary condition for the temperature, and we do not need the thermal conductivity coefficient κ to be large. The existence of...

A natural boundary element method for the Sobolev equation in the 2D unbounded domain

In this article, we devote ourselves to establishing a natural boundary element (NBE) method for the Sobolev equation in the 2D unbounded domain. To this end, we first constitute the time semi-discretized super-convergence format for the Sobolev equation by means of the Newmark method. Then, using the principle of natural boundary reduction, we establish a fully discretized NBE...

Fractional-order differential equations with anti-periodic boundary conditions: a survey

We will present an up-to-date review on anti-periodic boundary value problems of fractional-order differential equations and inclusions. Some recent and new results on nonlinear coupled fractional differential equations supplemented with coupled anti-periodic boundary conditions will also be highlighted.

Steady compressible heat-conductive fluid with inflow boundary condition

In this paper, we study strong solutions to the steady compressible heat-conductive fluid near a non-zero constant flow with the Dirichlet boundary condition for the velocity on the inflow and outflow part of the boundary. We also consider the Dirichlet boundary condition for the temperature, and we do not need the thermal conductivity coefficient κ to be large. The existence of...

A natural boundary element method for the Sobolev equation in the 2D unbounded domain

In this article, we devote ourselves to establishing a natural boundary element (NBE) method for the Sobolev equation in the 2D unbounded domain. To this end, we first constitute the time semi-discretized super-convergence format for the Sobolev equation by means of the Newmark method. Then, using the principle of natural boundary reduction, we establish a fully discretized NBE...