A unified treatment using critical pointmethods of the existence of multiple solutions for superlinear andsublinear Neumann problems

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

doi:10.3934/cpaa.2011.10.1791

Article Contents

2011, Volume 10, Issue 6: 1791-1816. Doi: 10.3934/cpaa.2011.10.1791

This issue Previous Article Even solutions of the Toda system with prescribed asymptotic behavior Next Article Nonexistence of nonconstant global minimizers with limit at $\infty$ of semilinear elliptic equations in all of $R^N$

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

1.
Département de Mathématiques, Université de Perpignan, Avenue de Villeneuve 52, 66860 Perpignan Cedex
2.
Department of Mathematics, National University of Ireland, University Road, Galway
3.
Department of Mathematics, National Technical University, Zografou Campus, Athens 15780

Received: May 2010

Revised: March 2011

Published: November 2011

Abstract / Introduction Related Papers Cited by

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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Mathematics Subject Classification: 35J20, 35J60, 58E05.

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