Existence of Solutions for a Fractional Laplacian Equation with Critical Nonlinearity

Zifei Shen and Fashun Gao

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: We study the fractional Laplacian equation (−Δ) su+λA(x)u=μu+|u|2*(s)-2u, x ∈ ℝN, here N > 2s, s ∈ (0, 1), 2*(s) = 2N/(N − 2s) is the critical exponent, and A(x) ≥ 0 is a real potential function. Employing the variational method we prove the existence of nontrivial solutions for μ small and λ large.

Date: 2013
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https://doi.org/10.1155/2013/638425

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:638425

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