Existence of nontrivial weak solutions for nonuniformly elliptic equation with mixed boundary condition in a variable exponent Sobolev space

Author:

Aramaki Junichi1ORCID

Affiliation:

1. Tokyo Denki University

Abstract

In In this paper, we consider a mixed boundary value problem for nonuniformly elliptic equation in a variable exponent Sobolev space containing p ( ) -Laplacian and mean curvature operator. More precisely, we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of a nontrivial weak solution and at least two nontrivial weak solutions according to some hypotheses on given functions.

Publisher

University of Szeged

Subject

Applied Mathematics

Reference28 articles.

1. J. Aramaki, Existence of three weak solutions for a class of quasi-linear elliptic operators with a mixed boundary value problem containing $p( )$-Laplacian in a variable exponent Sobolev space, submitted for publication.

2. J. Aramaki, Mixed boundary value problem for a class of quasi-linear elliptic operators containing $p( )$-Laplacian in a variable exponent Sobolev space, Adv. Math. Sci. Appl. 31(2022), No. 2, 207--239.

3. Existence of weak solutions for a nonlinear problem involving $$p(\cdot )$$-Laplacian operator with mixed boundary conditions

4. H. Brezis, Analyse fonctionelle. Theorie, methodes et applications, Masson, Paris, 1992.

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