The aim of this paper is investigating the existence and multiplicity of weak solutions to non-local equations involving a general integro-differential operator of fractional type, when the nonlinearity is subcritical and asymptotically linear at infinity. More precisely, in presence of an odd symmetric non-linear term, we prove multiplicity results by using a pseudo-index theory related to the genus. As a particular case we derive existence and multiplicity results for non-local equations involving the fractional Laplacian operator. Our theorems, obtained exploiting a novel abstract framework, extend to the non-local setting some results, already known in the literature, in the case of the classical Laplace operator.

A pseudo-index approach to fractional equations

Molica Bisci G
2015-01-01

Abstract

The aim of this paper is investigating the existence and multiplicity of weak solutions to non-local equations involving a general integro-differential operator of fractional type, when the nonlinearity is subcritical and asymptotically linear at infinity. More precisely, in presence of an odd symmetric non-linear term, we prove multiplicity results by using a pseudo-index theory related to the genus. As a particular case we derive existence and multiplicity results for non-local equations involving the fractional Laplacian operator. Our theorems, obtained exploiting a novel abstract framework, extend to the non-local setting some results, already known in the literature, in the case of the classical Laplace operator.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11576/2664286
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