TY - JOUR
T1 - 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
AU - Aramaki , Junichi
JO - Journal of Nonlinear Modeling and Analysis
VL - 1
SP - 107
EP - 132
PY - 2024
DA - 2024/03
SN - 6
DO - http://doi.org/10.12150/jnma.2024.107
UR - https://global-sci.org/intro/article_detail/jnma/22969.html
KW - $p(·)$-Laplacian type equation, three weak solutions, mixed boundary value problem.
AB - <p style="text-align: justify;">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.</p>