On the Existence of Solutions for the Critical Fractional Laplacian Equation in ℝN

Zifei Shen and Fashun Gao

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

Abstract: We study existence of solutions for the fractional Laplacian equation -Δsu+Vxu=u2*s-2u+fx, u in ℝN, u∈Hs(RN), with critical exponent 2*(s) = 2N/(N − 2s), N > 2s, s ∈ (0, 1), where V(x) ≥ 0 has a potential well and f : ℝN × ℝ → ℝ is a lower order perturbation of the critical power u2*s-2u. By employing the variational method, we prove the existence of nontrivial solutions for the equation.

Date: 2014
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https://doi.org/10.1155/2014/143741

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:143741

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