Existence of weak solutions for Kirchhoff type double-phase problem in R

Abstract

This article aims to study the existence of weak solutions for the Kirchhoff type double-phase problem imagewhere and is a real parameter. The main distinctive feature of this problem lies in the second nonlinearity on the right-hand side, which can be in the supercritical. Additionally, we encounter the Kirchhoff term, which might become zero at the origin. By imposing certain assumptions, we establish the existence and multiplicity results.