Schrödinger–Kirchhof-type problems involving the fractional p-Laplacian with exponential growth

Abstract

In this paper, we study the existence of a solution to Schrödinger–Kirchhoff-type problems involving a nonlocal integro-differential operator with the Trudinger–Moser nonlinearity. As a particular case, we consider the following fractional problem: where is a continuous function with some appropriate assumptions, is the fractional p-Laplacian, with sp = N, K, V are positive continuous functions satisfying some additional conditions, f is a continuous function on with exponential growth. By using the mountain pass theorem, we obtain the existence of solutions to the above problem in suitable Sobolev space. A novel feature of our paper is that the above problem may be degenerate, that is, the Kirchhoff function .