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

Motreanu, D.
; 
O'Regan, Donal
; 
Papageorgiou, Nikolaos S.
Identifiers
http://hdl.handle.net/10379/12996
https://doi.org/10.13025/28220
Repository DOI
10.3934/cpaa.2011.10.1791
Publication Date
2011-05-01
Keywords
superlinear and sublinear problems, critical point theory, truncation techniques, upper-lower solutions, morse theory, gradient flow, multiple solutions, semilinear elliptic-equations, boundary-value-problems, unique continuation, local minimizers, resonance, sign
Type
Article
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Citation
Motreanu, D. O'Regan, Donal; Papageorgiou, Nikolaos S. (2011). A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear neumann problems. Communications on Pure and Applied Analysis 10 (6), 1791-1816
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 flow, we show that the problem can have seven nontrivial smooth solutions, four of which have constant sign and three are nodal.
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Publisher
American Institute of Mathematical Sciences (AIMS)
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Externally hosted open access publications with University of Galway authors (2)