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 (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we consider a mixed boundary value problem toa class of nonlinear operators containing $p(·)$-Laplacian. More precisely, weare concerned with the problem with the Dirichlet condition on a part ofthe boundary and the Steklov boundary condition on an another part of theboundary. We show the existence of at least three weak solutions under somehypotheses on given functions and the values of parameters.
Keywords: $p(·)$-Laplacian type equation; three weak solutions; mixed boundary value problem.