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Advances in Nonlinear Analysis

Editor-in-Chief: Radulescu, Vicentiu / Squassina, Marco


IMPACT FACTOR 2018: 6.636

CiteScore 2018: 5.03

SCImago Journal Rank (SJR) 2018: 3.215
Source Normalized Impact per Paper (SNIP) 2018: 3.225

Mathematical Citation Quotient (MCQ) 2017: 1.89

Open Access
Online
ISSN
2191-950X
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Multi-bump solutions for a Kirchhoff-type problem

Claudianor O. Alves
  • Corresponding author
  • Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática, CEP 58429-900, Campina Grande - Pb, Brazil
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/ Giovany M. Figueiredo
Published Online: 2015-11-12 | DOI: https://doi.org/10.1515/anona-2015-0101

Abstract

In this paper, we study the existence of solutions for the Kirchhoff problem M(3|u|2dx+3(λa(x)+1)u2dx)(-Δu+(λa(x)+1)u)=f(u) in ℝ3, uH1(ℝ3) Assuming that the nonnegative function a(x) has a potential well with int (a -1({0})) consisting of k disjoint components Ω12,...,Ωk and the nonlinearity f(t) has a subcritical growth, we are able to establish the existence of positive multi-bump solutions by using variational methods.

Keywords: Kirchhoff problem; multi-bump solution; variational methods

MSC: 35J65; 34B15

About the article

Received: 2015-07-27

Accepted: 2015-09-30

Published Online: 2015-11-12

Published in Print: 2016-02-01


Funding Source: CNPq

Award identifier / Grant number: 301807/2013-2

Funding Source: INCT-MAT

Funding Source: CNPq

Award identifier / Grant number: 302933/2014-0


Citation Information: Advances in Nonlinear Analysis, Volume 5, Issue 1, Pages 1–26, ISSN (Online) 2191-950X, ISSN (Print) 2191-9496, DOI: https://doi.org/10.1515/anona-2015-0101.

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Citing Articles

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[1]
Guoqing Chai and Weiming Liu
Boundary Value Problems, 2018, Volume 2018, Number 1
[2]
Claudianor O. Alves and Ailton R. da Silva
Acta Applicandae Mathematicae, 2017

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