Existence of solutions for nonlocal Schrödinger–Kirchhoff problems with critical Trudinger–Moser nonlinearity

Abstract

In this paper, we are concerned with solutions for nonlocal Schrödinger–Kirchhoff problems with critical Trudinger–Moser nonlinearity on a bounded domain with Lipschitz boundary. With the help of the minimax method, the fractional Trudinger–Moser inequality, Ekeland's variational principle, and other techniques, we establish an existence theorem for a nonnegative solution with positive energy to a class of nonlocal Schrödinger–Kirchhoff problems and an existence theorem for a nontrivial solution with negative energy to another class of nonlocal Schrödinger–Kirchhoff problems.