Three weak solutions for nonlocal fractional Laplacian equations (Q1725039)

Summary: The existence of three weak solutions for the following nonlocal fractional equation \((- \Delta)^s u - \lambda u = \mu f(x, u)\) in \(\Omega, u = 0\) in \(\mathbb{R}^n \smallsetminus \Omega\), is investigated, where \(s \in(0,1)\) is fixed, \((- \Delta)^s\) is the fractional Laplace operator, \(\lambda\) and \(\mu\) are real parameters, \(\Omega\) is an open bounded subset of \(\mathbb{R}^n\), \(n > 2 s\), and the function \(f\) satisfies some regularity and natural growth conditions. The approach is based on a three-critical-point theorem for differential functionals.