Multiple solutions to fractional equations without the Ambrosetti-Rabinowitz condition

Abstract

In this article we study a class of fractional Laplace equations which do not satisfy the Ambrosetti-Rabinowitz condition (AR-condition). We establish the existence of three nontrivial solutions and of multiple sign changing solutions by using Morse theory.

Keywords

• Fractional Laplacian
• Morse theory
• sign changing solution
• improved subcritical polynomial growth