Infinitely many solutions for a class of $$p(\kappa )$$-Kirchhoff type problems involving Steklov boundary conditions

The aim of this paper is to investigate the existence of solutions for p(κ)-Kirchhofftype problems with Steklov boundary conditions. By imposing appropriate conditions on the Kirchhoff function and the nonlinearities, we demonstrate the existence of an infinite number of weak solutions to the problem within variable exponent Sobolev spaces. Our approach is based on critical point theory in conjunction with a variational principle introduced by Bonanno and Molica Bisci (Bound Value Probl 2009:1–20, 2009). Additionally, we seek to extend and refine several recent results in the literature.