Multiplicity and concentration of solutions for a fractional Schrödinger equation via Nehari method and pseudo-index theory

Abstract

We study a nonlinear fractional Schrödinger equation motivated by nonlocal quantum mechanics. Under suitable assumptions on the potentials, we explore the existence, concentration, convergence, and decay estimates of ground state solutions for this equation. Moreover, the multiplicity of solutions is constructed via pseudo-index theory, and the existence of sign-changing solutions is obtained via the Nehari method.