Open AccessA unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear Neumann problems
Author(s) -
Dumitru Motreanu,
Donal O’Regan,
Nikolaos S. Papageorgiou
Publication year - 2011
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2011.10.1791
Subject(s) - sublinear function , mathematics , constant (computer programming) , sign (mathematics) , morse theory , critical point (mathematics) , truncation (statistics) , neumann boundary condition , mathematical analysis , pure mathematics , computer science , boundary value problem , programming language , statistics
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