Infinitely many high energy solutions for fractional Schrödinger equations with magnetic field

Abstract

In this paper we investigate the existence of infinitely many solutions for nonlocal Schrödinger equation involving a magnetic potential continuous function, and (-) sA is the fractional magnetic operator. Under suitable assumptions for the potential function V and nonlinearity f , we obtain the existence of infinitely many nontrivial high energy solutions by using the variant fountain theorem. MSC: 35R11; 35A15; 35J60; 47G20

Multiplicity Results of Solutions to Non-Local Magnetic Schrödinger–Kirchhoff Type Equations in RN

“…Proof. The proof follows the lines of that of Lemma 3.2 in [51]. To apply Lemma 7, let us denote E := H s A,V (R N , C) and I := J λ .…”