Multiple solutions for p-Laplacian type equations

A. Kristály, Hannelore Lisei, Csaba Varga

Research output: Contribution to journalArticle

48 Citations (Scopus)

Abstract

In this paper we establish the existence of three weak solutions of an equation which involves a general elliptic operator in divergence form (in particular, a p-Laplacian operator), while the nonlinearity has a (p - 1)-sublinear growth at infinity. This result completes some recent papers, where mountain pass type solutions were obtained providing the nonlinear term via a (p - 1)-superlinear growth at infinity (fulfilling an Ambrosetti-Rabinowitz type condition). In our case, an abstract critical point result is applied, proved by G. Bonanno [G. Bonanno, Some remarks on a three critical points theorem, Nonlinear Analysis 54 (2003) 651-665].

Original languageEnglish
Pages (from-to)1375-1381
Number of pages7
JournalNonlinear Analysis
Volume68
Issue number5
DOIs
Publication statusPublished - Mar 1 2008

Fingerprint

Multiple Solutions
P-Laplacian
Critical point
Infinity
Mountain Pass
P-Laplacian Operator
Nonlinear analysis
Nonlinear Analysis
Elliptic Operator
Weak Solution
Divergence
Nonlinearity
Term
Theorem
Form

Keywords

  • (p - 1)-Sublinearity at infinity
  • Divergence type operator
  • Multiple solutions
  • p-Laplacian

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Multiple solutions for p-Laplacian type equations. / Kristály, A.; Lisei, Hannelore; Varga, Csaba.

In: Nonlinear Analysis, Vol. 68, No. 5, 01.03.2008, p. 1375-1381.

Research output: Contribution to journalArticle

Kristály, A. ; Lisei, Hannelore ; Varga, Csaba. / Multiple solutions for p-Laplacian type equations. In: Nonlinear Analysis. 2008 ; Vol. 68, No. 5. pp. 1375-1381.
@article{e85f9057987b428bb7aaa15e2f16c850,
title = "Multiple solutions for p-Laplacian type equations",
abstract = "In this paper we establish the existence of three weak solutions of an equation which involves a general elliptic operator in divergence form (in particular, a p-Laplacian operator), while the nonlinearity has a (p - 1)-sublinear growth at infinity. This result completes some recent papers, where mountain pass type solutions were obtained providing the nonlinear term via a (p - 1)-superlinear growth at infinity (fulfilling an Ambrosetti-Rabinowitz type condition). In our case, an abstract critical point result is applied, proved by G. Bonanno [G. Bonanno, Some remarks on a three critical points theorem, Nonlinear Analysis 54 (2003) 651-665].",
keywords = "(p - 1)-Sublinearity at infinity, Divergence type operator, Multiple solutions, p-Laplacian",
author = "A. Krist{\'a}ly and Hannelore Lisei and Csaba Varga",
year = "2008",
month = "3",
day = "1",
doi = "10.1016/j.na.2006.12.031",
language = "English",
volume = "68",
pages = "1375--1381",
journal = "Nonlinear Analysis, Theory, Methods and Applications",
issn = "0362-546X",
publisher = "Elsevier Limited",
number = "5",

}

TY - JOUR

T1 - Multiple solutions for p-Laplacian type equations

AU - Kristály, A.

AU - Lisei, Hannelore

AU - Varga, Csaba

PY - 2008/3/1

Y1 - 2008/3/1

N2 - In this paper we establish the existence of three weak solutions of an equation which involves a general elliptic operator in divergence form (in particular, a p-Laplacian operator), while the nonlinearity has a (p - 1)-sublinear growth at infinity. This result completes some recent papers, where mountain pass type solutions were obtained providing the nonlinear term via a (p - 1)-superlinear growth at infinity (fulfilling an Ambrosetti-Rabinowitz type condition). In our case, an abstract critical point result is applied, proved by G. Bonanno [G. Bonanno, Some remarks on a three critical points theorem, Nonlinear Analysis 54 (2003) 651-665].

AB - In this paper we establish the existence of three weak solutions of an equation which involves a general elliptic operator in divergence form (in particular, a p-Laplacian operator), while the nonlinearity has a (p - 1)-sublinear growth at infinity. This result completes some recent papers, where mountain pass type solutions were obtained providing the nonlinear term via a (p - 1)-superlinear growth at infinity (fulfilling an Ambrosetti-Rabinowitz type condition). In our case, an abstract critical point result is applied, proved by G. Bonanno [G. Bonanno, Some remarks on a three critical points theorem, Nonlinear Analysis 54 (2003) 651-665].

KW - (p - 1)-Sublinearity at infinity

KW - Divergence type operator

KW - Multiple solutions

KW - p-Laplacian

UR - http://www.scopus.com/inward/record.url?scp=43049112839&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=43049112839&partnerID=8YFLogxK

U2 - 10.1016/j.na.2006.12.031

DO - 10.1016/j.na.2006.12.031

M3 - Article

AN - SCOPUS:43049112839

VL - 68

SP - 1375

EP - 1381

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 5

ER -