Nonlocal Neumann Boundary Value Problem for Fractional Symmetric Hahn Integrodifference Equations

In this article, we present a nonlocal Neumann boundary value problems for separate sequential fractional symmetric Hahn integrodifference equation. The problem contains five fractional symmetric Hahn difference operators and one fractional symmetric Hahn integral of different orders. We employ Banach fixed point theorem and Schauder’s fixed point theorem to study the existence results of the problem.

On solvability of the Dirichlet and Neumann boundary value problems for the Poisson equation with multiple involution

Transformations of the involution type are considered in the space $R^l$, $l\geq 2$. The matrix properties of these transformations are investigated. The structure of the matrix under consideration is determined and it is proved that the matrix of these transformations is determined by the elements of the first row. Also, the symmetry of the matrix under study is proved. In addition, the eigenvectors and eigenvalues of the matrix under consideration are found explicitly. The inverse matrix is also found and it is proved that the inverse matrix has the same structure as the main matrix. The properties of the nonlocal analogue of the Laplace operator are introduced and studied as applications of the transformations under consideration. For the corresponding nonlocal Poisson equation in the unit ball, the solvability of the Dirichlet and Neumann boundary value problems is investigated. A theorem on the unique solvability of the Dirichlet problem is proved, an explicit form of the Green's function and an integral representation of the solution are constructed, and the order of smoothness of the solution of the problem in the Hölder class is found. Necessary and sufficient conditions for the solvability of the Neumann problem, an explicit form of the Green's function, and the integral representation are also found.

Multiplicity of solutions for a nonlocal nonhomogeneous Neumann boundary problem with two critical exponents

This article concerns the multiplicity of solutions for a class of nonlocal and nonhomogeneous Neumann boundary value problems involving the p ( x )-Laplacian, in which both nonlinear terms assume critical growth. We use variational method, exploring an important truncation argument and properties of the genus.

Solutions to Neumann boundary value problems with a generalized 𝑝-Laplacian

The purpose of this work is to investigate the existence of solutions for various Neumann boundary value problems associated to the Laplacian-type operators. The main results are obtained using the extension of Mawhin’s continuation theorem.

Topological degree methods for a Neumann problem governed by nonlinear elliptic equation

In this paper, we will use the topological degree, introduced by Berkovits, to prove existence of weak solutions to a Neumann boundary value problems for the following nonlinear elliptic equation- div\,\,a\left( {x,u,\nabla u} \right) = b\left( x \right){\left| u \right|^{p - 2}}u + \lambda H\left( {x,u,\nabla u} \right),where Ω is a bounded smooth domain of 𝕉N.

On an approximate solution of a class of surface singular integral equations of the first kind

In this work, a method for calculating an approximate solution of a singular integral equation of first kind is presented for the Neumann boundary value problems for the Helmholtz equation.