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
Year: 2024
Author: Junichi Aramaki
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 1 : pp. 107–132
Abstract
In this paper, we consider a mixed boundary value problem to a class of nonlinear operators containing $p(·)$-Laplacian. 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 at least three weak solutions under some hypotheses on given functions and the values of parameters.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2024.107
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 1 : pp. 107–132
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: $p(·)$-Laplacian type equation three weak solutions mixed boundary value problem.