Three Weak Solutions for Nonlocal Fractional Laplacian Equations
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 sati...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/809769 |
| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |