Multiplicity and concentration of solutions to a fractional p-Laplace problem with exponential growth

In this paper, we study the Schrodinger equation involving the Ns-fractional Laplacian: epsilon N(-Delta)sN/su + V (x)|u| Ns -2u = f (u) in RN, where epsilon is a positive parameter, N = ps, s is an element of (0, 1). The nonlinear function f has exponential growth and the potential function V is a continuous function satisfying some suitable conditions. Our problem lacks compactness. By using the Ljusternik-Schnirelmann theory, we obtain the existence, multiplicity and concentration of nontrivial nonnegative solutions for small values of the parameter.

Automated summary

In this paper, we study the existence, multiplicity, and concentration of nontrivial nonnegative solutions of the Schrödinger equation involving the fractional Laplacian. By using the Ljusternik-Schnirelmann theory, we obtain these results for small values of the parameter.