Three Weak Solutions for Nonlocal Fractional Laplacian Equations

Dandan Yang and Chuanzhi Bai

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: The existence of three weak solutions for the following nonlocal fractional equation (−Δ) su − λu = μf(x, u) in Ω, u = 0 in ℝn∖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 ℝn, n > 2s, and the function f satisfies some regularity and natural growth conditions. The approach is based on a three‐critical‐point theorem for differential functionals.

Date: 2014
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https://doi.org/10.1155/2014/809769

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:809769

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