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Communications on Pure and Applied Analysis (CPAA)
 

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

Pages: 1791 - 1816, Volume 10, Issue 6, November 2011

doi:10.3934/cpaa.2011.10.1791       Abstract        References        Full Text (502.0K)       Related Articles

D. Motreanu - Département de Mathématiques, Université de Perpignan, Avenue de Villeneuve 52, 66860 Perpignan Cedex, France (email)
Donal O'Regan - Department of Mathematics, National University of Ireland, University Road, Galway, Ireland (email)
Nikolaos S. Papageorgiou - Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece (email)

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.

Keywords:  Superlinear and sublinear problems, critical point theory, truncation techniques, upper-lower solutions, Morse theory, gradient flow, multiple solutions.
Mathematics Subject Classification:  35J20, 35J60, 58E05.

Received: May 2010;      Revised: March 2011;      Published: May 2011.

 References