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2014 On the Existence of Solutions for the Critical Fractional Laplacian Equation in N
Zifei Shen, Fashun Gao
Abstr. Appl. Anal. 2014: 1-10 (2014). DOI: 10.1155/2014/143741

Abstract

We study existence of solutions for the fractional Laplacian equation -Δsu+Vxu=u2*s-2u+fx, u in N, uHs(RN), with critical exponent 2*s=2N/(N-2s), N>2s, s0, 1, where Vx0 has a potential well and f:N× 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.

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Zifei Shen. Fashun Gao. "On the Existence of Solutions for the Critical Fractional Laplacian Equation in N." Abstr. Appl. Anal. 2014 1 - 10, 2014. https://doi.org/10.1155/2014/143741

Information

Published: 2014
First available in Project Euclid: 26 March 2014

zbMATH: 07021805
MathSciNet: MR3166568
Digital Object Identifier: 10.1155/2014/143741

Rights: Copyright © 2014 Hindawi

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