In this paper, we are concerned with the problem driven by a non-local integro-differential operator with homogeneous Dirichlet boundary conditions. As a particular case, we study multiple solutions for the following non-local fractional Laplace equations:where is fixed parameter, is an open bounded subset of with smooth boundary () and is the fractional Laplace operator. By a variant version of the Mountain Pass Theorem, a multiplicity result is obtained for the above-mentioned superlinear problem without Ambrosetti-Rabinowitz condition. Consequently, the result may be looked as a complete extension of the previous work of Wang and Tang to the non-local fractional setting.

Multiplicity of solutions for a class of superlinear non-local fractional equations

FERRARA, Massimiliano
Validation
;
2015-01-01

Abstract

In this paper, we are concerned with the problem driven by a non-local integro-differential operator with homogeneous Dirichlet boundary conditions. As a particular case, we study multiple solutions for the following non-local fractional Laplace equations:where is fixed parameter, is an open bounded subset of with smooth boundary () and is the fractional Laplace operator. By a variant version of the Mountain Pass Theorem, a multiplicity result is obtained for the above-mentioned superlinear problem without Ambrosetti-Rabinowitz condition. Consequently, the result may be looked as a complete extension of the previous work of Wang and Tang to the non-local fractional setting.
2015
integrodifferential operator; Mountain Pass Theorem; superlinear condition; fractional Laplacian
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/6081
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