A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear neumann problems

Dumitru Motreanu; Donal O'Regan; Nikolaos S. Papageorgiou

doi:10.3934/cpaa.2011.10.1791

A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear neumann problems

Dumitru Motreanu
, Donal O'Regan
, Nikolaos S. Papageorgiou

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

13 Citations (Scopus)

Abstract

In this paper we present a framework which permits the unified treatment of the existence of multiple solutions for superlinear and sublinear Neumann problems. Using critical point theory, truncation techniques, the method of upper-lower solutions, Morse theory and the invariance properties of the negative gradient ow, we show that the problem can have seven nontrivial smooth solutions, four of which have constant sign and three are nodal.

Original language	English
Pages (from-to)	1791-1816
Number of pages	26
Journal	Communications on Pure and Applied Analysis
Volume	10
Issue number	6
DOIs	https://doi.org/10.3934/cpaa.2011.10.1791
Publication status	Published - 1 Nov 2011

Keywords

Critical point theory
Gradient ow
Morse theory
Multiple solutions
Superlinear and sublinear problems
Truncation techniques
Upper-lower solutions

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Motreanu, D,O'Regan, D,Papageorgiou, NS

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10.3934/cpaa.2011.10.1791

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abstract = "In this paper we present a framework which permits the unified treatment of the existence of multiple solutions for superlinear and sublinear Neumann problems. Using critical point theory, truncation techniques, the method of upper-lower solutions, Morse theory and the invariance properties of the negative gradient ow, we show that the problem can have seven nontrivial smooth solutions, four of which have constant sign and three are nodal.",

keywords = "Critical point theory, Gradient ow, Morse theory, Multiple solutions, Superlinear and sublinear problems, Truncation techniques, Upper-lower solutions",

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A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear neumann problems. / Motreanu, Dumitru; O'Regan, Donal; Papageorgiou, Nikolaos S.
In: Communications on Pure and Applied Analysis, Vol. 10, No. 6, 01.11.2011, p. 1791-1816.

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

TY - JOUR

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AU - Motreanu, Dumitru

AU - O'Regan, Donal

AU - Papageorgiou, Nikolaos S.

PY - 2011/11/1

Y1 - 2011/11/1

N2 - In this paper we present a framework which permits the unified treatment of the existence of multiple solutions for superlinear and sublinear Neumann problems. Using critical point theory, truncation techniques, the method of upper-lower solutions, Morse theory and the invariance properties of the negative gradient ow, we show that the problem can have seven nontrivial smooth solutions, four of which have constant sign and three are nodal.

AB - In this paper we present a framework which permits the unified treatment of the existence of multiple solutions for superlinear and sublinear Neumann problems. Using critical point theory, truncation techniques, the method of upper-lower solutions, Morse theory and the invariance properties of the negative gradient ow, we show that the problem can have seven nontrivial smooth solutions, four of which have constant sign and three are nodal.

KW - Critical point theory

KW - Gradient ow

KW - Morse theory

KW - Multiple solutions

KW - Superlinear and sublinear problems

KW - Truncation techniques

KW - Upper-lower solutions

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U2 - 10.3934/cpaa.2011.10.1791

DO - 10.3934/cpaa.2011.10.1791

M3 - Article

SN - 1534-0392

VL - 10

SP - 1791

EP - 1816

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 6

ER -

A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear neumann problems

Abstract

Keywords

Authors (Note for portal: view the doc link for the full list of authors)

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