A pseudo-index approach to fractional equations

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• 作者：Rossella Bartolo^a ; ^{rossella.bartolo@poliba.it" class="auth_mail" title="E-mail the corresponding author} ; Giovanni Molica Bisci^b ; ^{gmolica@unirc.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 49J35 ; 35A15 ; 35S15 ; 58E05 ; secondary ; 47G20 ; 45G05
• 刊名：Expositiones Mathematicae
• 出版年：2015
• 出版时间：2015
• 年：2015
• 卷：33
• 期：4
• 页码：502-516
• 全文大小：230 K

文摘

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.