Multiplicity results for elliptic Kirchhoff-type problems-Reference-Cited by-同舟云学术

Multiplicity results for elliptic Kirchhoff-type problems

Published:2017-02-01 Issue:1 Volume:6 Page:85-93
ISSN:2191-9496
Container-title:Advances in Nonlinear Analysis
language:
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Author:

Baraket Sami¹,Molica Bisci Giovanni²

Affiliation:

1. 1Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, 11451 Riyadh, Saudi Arabia

2. 2Dipartimento Patrimonio, Architettura, Urbanistica, Università degli Studi Mediterranea di Reggio Calabria, Salita Melissari – Feo di Vito, 89100 Reggio Calabria, Italy

Abstract

AbstractThe aim of this paper is to establish the existence of multiple solutions for a perturbed Kirchhoff-type problem depending on two real parameters. More precisely, we show that an appropriate oscillating behaviour of the nonlinear part, even under small perturbations, ensures the existence of at least three nontrivial weak solutions. Our approach combines variational methods with properties of nonlocal fractional operators.

Funder

National Plan of Sciences, Technology and Innovation (MAARIFAH)

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Link

https://www.degruyter.com/downloadpdf/journals/anona/6/1/article-p85.xml

Reference42 articles.

1. Positive solutions for a nonlinear nonlocal elliptic transmission problem;App. Math. Lett.,2003

2. Multiplicity results for elliptic fractional equations with subcritical term;NoDEA Nonlinear Differential Equations Appl.,2015

3. Existence results of positive solutions of Kirchhoff type problems;Nonlinear Anal.,2009