Multiple Solutions for Superlinear Fractional Problems via Theorems of Mixed Type

Abstract

In this paper we investigate the existence of multiple solutions for the following two fractional problemswhere s ∈ (0, 1), N > 2s, Ω is a smooth bounded domain of R N , and f :Ω × R → R is a superlinear continuous function which does not satisfy the well-known Ambrosetti-Rabinowitz condition. Here (−∆Ω) s is the spectral Laplacian and (−∆ R N ) s is the fractional Laplacian in R N . By applying variational theorems of mixed type due to Marino and Saccon and the Linking Theorem, we prove the existence of multiple solutions for the above problems.2010 Mathematics Subject Classification. 35A15, 35J60, 35R11, 45G05.