Three Weak Solutions for Nonlocal Fractional Laplacian Equations

Abstract EN

The existence of three weak solutions for the following nonlocal fractional equation ( - Δ ) s u - λ u = μ f ( x , u ) in Ω , u = 0 in ℝ n ∖ Ω , is investigated, where s ∈ ( 0,1 ) is fixed, ( - Δ ) s is the fractional Laplace operator, λ and μ are real parameters, Ω is an open bounded subset of 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.