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2014 Existence Results for a Perturbed Problem Involving Fractional Laplacians
Yan Hu
Abstr. Appl. Anal. 2014: 1-10 (2014). DOI: 10.1155/2014/548301


We extend the results of Cabre and Sire (2011) to show the existence of layer solutions of fractional Laplacians with perturbed nonlinearity (-Δ)su=b(x)f(u) in with s(0,1). Here b is a positive periodic perturbation for f, and -f is the derivative of a balanced well potential G. That is, GC2,γ satisfies G(1)=G(-1)<G(τ)τ(-1,1), G'(1)=G'(-1)=0. First, for odd nonlinearity f and for every s(0,1), we prove that there exists a layer solution via the monotone iteration method. Besides, existence results are obtained by variational methods for s(1/2,1) and for more general nonlinearities. While the case s1/2 remains open.


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Yan Hu. "Existence Results for a Perturbed Problem Involving Fractional Laplacians." Abstr. Appl. Anal. 2014 1 - 10, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022604
MathSciNet: MR3191052
Digital Object Identifier: 10.1155/2014/548301

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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