Kirchhoff-Type Problem with Mixed Boundary Condition in a Variable Exponent Sobolev Space (Communications in Mathematical Research, 2023)
In this paper, we consider a mixed boundary value problem for thestationary Kirchhoff-type equation containing $p(·)$-Laplacian. More precisely,we are 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 one, two or infinitely many nontrivial weak solutions according to hypotheses on given functions.