Abstract and Applied Analysis

Three Weak Solutions for Nonlocal Fractional Laplacian Equations

Dandan Yang and Chuanzhi Bai

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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 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 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.

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Abstr. Appl. Anal., Volume 2014 (2014), Article ID 809769, 7 pages.

First available in Project Euclid: 26 March 2014

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Yang, Dandan; Bai, Chuanzhi. Three Weak Solutions for Nonlocal Fractional Laplacian Equations. Abstr. Appl. Anal. 2014 (2014), Article ID 809769, 7 pages. doi:10.1155/2014/809769. https://projecteuclid.org/euclid.aaa/1395858529

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