Perturbation methods for nonlocal Kirchhoff–type problems-Reference-Cited by-同舟云学术

Perturbation methods for nonlocal Kirchhoff–type problems

Published:2017-08-01 Issue:4 Volume:20 Page:829-853
ISSN:1311-0454
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

D’Onofrio Luigi¹,Fiscella Alessio²,Molica Bisci Giovanni³

Affiliation:

1. Dipartimento di Studi Aziendali e Quantitativi Università degli Studi di Napoli “Parthenope” Via Parisi 13, 80100 Napoli , Italy

2. Departamento de Matemática , Universidade Estadual de Campinas IMECC , Rua Sérgio Buarque de Holanda , Campinas , 651 SP CEP 13083–859 , Brazil

3. Dipartimento PAU , Università “Mediterranea” di Reggio Calabria Via Melissari 24, 89124 Reggio Calabria , Italy

Abstract

Abstract This paper deals with the existence of infinitely many solutions for a class of Dirichlet elliptic problems driven by a bi–nonlocal operator u ↦ M(∥u∥2)(−Δ) su, where M models a Kirchhoff–type coefficient while (−Δ) 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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2017-0044/pdf

Reference32 articles.

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