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Existence Results for a Perturbed Problem Involving Fractional Laplacians

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  • Yan Hu

Abstract

We extend the results of Cabre and Sire (2011) to show the existence of layer solutions of fractional Laplacians with perturbed nonlinearity in with . Here is a positive periodic perturbation for , and is the derivative of a balanced well potential . That is, satisfies First, for odd nonlinearity and for every , we prove that there exists a layer solution via the monotone iteration method. Besides, existence results are obtained by variational methods for and for more general nonlinearities. While the case remains open.

Suggested Citation

  • Yan Hu, 2014. "Existence Results for a Perturbed Problem Involving Fractional Laplacians," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, March.
    • Handle: RePEc:hin:jnlaaa:548301
    DOI: 10.1155/2014/548301
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