Multiple nontrivial solutions for neumann problems involving the p-laplacian: A morse theoretical approach

A. Kristály, Nikolaos S. Papageorgiou

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We consider nonlinear elliptic Neumann problems driven by the p-Laplacian. Using variational techniques together with Morse theory (in particular, critical groups and the Poincaré-Hopf formula), we prove some multiplicity results: either three or four distinct nontrivial solutions are guaranteed, depending on the geometry and smoothness of the nonlinear term.

Original languageEnglish
Pages (from-to)83-107
Number of pages25
JournalAdvanced Nonlinear Studies
Volume10
Issue number1
Publication statusPublished - Feb 2010

Fingerprint

Neumann problem
Neumann Problem
P-Laplacian
Nontrivial Solution
Critical Group
Morse Theory
Multiplicity Results
geometry
Elliptic Problems
Smoothness
Distinct
Term

Keywords

  • Morse theory
  • Multiple solutions.
  • Neumann problem
  • P-Laplacian

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematics(all)

Cite this

Multiple nontrivial solutions for neumann problems involving the p-laplacian : A morse theoretical approach. / Kristály, A.; Papageorgiou, Nikolaos S.

In: Advanced Nonlinear Studies, Vol. 10, No. 1, 02.2010, p. 83-107.

Research output: Contribution to journalArticle

@article{8405d7e40a51426a99d1b31404057e23,
title = "Multiple nontrivial solutions for neumann problems involving the p-laplacian: A morse theoretical approach",
abstract = "We consider nonlinear elliptic Neumann problems driven by the p-Laplacian. Using variational techniques together with Morse theory (in particular, critical groups and the Poincar{\'e}-Hopf formula), we prove some multiplicity results: either three or four distinct nontrivial solutions are guaranteed, depending on the geometry and smoothness of the nonlinear term.",
keywords = "Morse theory, Multiple solutions., Neumann problem, P-Laplacian",
author = "A. Krist{\'a}ly and Papageorgiou, {Nikolaos S.}",
year = "2010",
month = "2",
language = "English",
volume = "10",
pages = "83--107",
journal = "Advanced Nonlinear Studies",
issn = "1536-1365",
publisher = "Advanced Nonlinear Studies",
number = "1",

}

TY - JOUR

T1 - Multiple nontrivial solutions for neumann problems involving the p-laplacian

T2 - A morse theoretical approach

AU - Kristály, A.

AU - Papageorgiou, Nikolaos S.

PY - 2010/2

Y1 - 2010/2

N2 - We consider nonlinear elliptic Neumann problems driven by the p-Laplacian. Using variational techniques together with Morse theory (in particular, critical groups and the Poincaré-Hopf formula), we prove some multiplicity results: either three or four distinct nontrivial solutions are guaranteed, depending on the geometry and smoothness of the nonlinear term.

AB - We consider nonlinear elliptic Neumann problems driven by the p-Laplacian. Using variational techniques together with Morse theory (in particular, critical groups and the Poincaré-Hopf formula), we prove some multiplicity results: either three or four distinct nontrivial solutions are guaranteed, depending on the geometry and smoothness of the nonlinear term.

KW - Morse theory

KW - Multiple solutions.

KW - Neumann problem

KW - P-Laplacian

UR - http://www.scopus.com/inward/record.url?scp=77955874676&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955874676&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:77955874676

VL - 10

SP - 83

EP - 107

JO - Advanced Nonlinear Studies

JF - Advanced Nonlinear Studies

SN - 1536-1365

IS - 1

ER -