A pseudo-index approach to fractional equations

被引:5
作者
Bartolo, Rossella [1 ]
Bisci, Giovanni Molica [2 ]
机构
[1] Politecn Bari, Dipartimento Meccan Matemat & Management, I-70125 Bari, Italy
[2] Univ Mediterranea Reggio Calabria, Dipartimento PAU, I-89100 Reggio Di Calabria, Italy
关键词
Fractional Laplacian; Integro-differential operator; Variational methods; Asymptotically linear problem; Pseudo-genus; RESONANCE;
D O I
10.1016/j.exmath.2014.12.001
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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. (C) 2014 Elsevier GmbH. All rights reserved.
引用
收藏
页码:502 / 516
页数:15
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