On Kirchhoff-type p(.)-Laplacian problems with sandwich-type and arbitrary growth

Abstract

We establish the existence of a positive bounded weak solution for a class of Kirchhoff-type $p(\cdot )$-Laplacian problems involving an arbitrary growth and a sandwich-type growth $s(\cdot )\in (\inf p,\sup p)$. This setting leads to substantial analytical difficulties in the variational analysis of the associated energy functional. By combining truncation arguments with a priori estimates, we prove the existence result under suitable assumptions on the data.