One‐dimensional periodic fractional Schrödinger equations with exponential critical growth

Abstract

In the present paper, we study the existence of nontrivial solutions of the following one‐dimensional fractional Schrödinger equation where stands for the 1/2‐Laplacian, , and is a continuous function with an exponential critical growth. Comparing with the existing works in the field of exponential‐critical‐growth fractional Schrödinger equations, we encounter some new challenges due to the weaker assumptions on the reaction term . By using some sharp energy estimates, we present a detailed analysis of the energy level, which allows us to establish the existence of nontrivial solutions for a wider class of nonlinear terms. Furthermore, we use the non‐Nehari manifold method to establish the existence of Nehari‐type ground state solutions of the one‐dimensional fractional Schrödinger equations.