PERTURBATION METHODS FOR NONLOCAL KIRCHHOFF-TYPE PROBLEMS

被引：14
|
作者：
D'Onofrio, Luigi [1 ]
Fiscella, Alessio [2 ]
Bisci, Giovanni Molica [3 ]
机构：
[1] Univ Napoli Parthenope, Dipartimento Studi Aziendali & Quantitat, Via Parisi 13, I-80100 Naples, Italy
[2] Univ Estadual Campinas, IMECC, Dept Matemat, Rua Sergio Buarque Holanda,651 Campinas, BR-13083859 Campinas, SP, Brazil
[3] Univ Mediterranea Reggio Calabria, Dipartimento PAU, Via Melissari 24, I-89124 Reggio Di Calabria, Italy
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2017年 / 20卷 / 04期
关键词：
Kirchhoff-type problems; existence of solutions; fractional Sobolev spaces; variational methods; MULTIPLICITY; EXISTENCE; EQUATIONS;
D O I：
10.1515/fca-2017-0044
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper deals with the existence of infinitely many solutions for a class of Dirichlet elliptic problems driven by a bi-nonlocal operator u bar right arrow M(parallel to u parallel to(2))(-Delta)(s)u, where M models a Kirchhoff-type coefficient while (-Delta)(s) denotes the fractional Laplace operator. More precisely, by adapting to our bi-nonlocal framework the variational and topological tools introduced in [16], we establish the existence of infinitely many solutions. The main feature and difficulty of our problems is due to the possible degenerate nature of the Kirchhoff term M.
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页码：829 / 853
页数：25
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