Multiple solutions of Neumann elliptic problems with critical nonlinearity

Pages: 301 - 320, Volume 5, Issue 2, April 1999

doi:10.3934/dcds.1999.5.301       Abstract        Full Text (267.3K)       Related Articles

Monica Musso - Dipartimento di Matematica, Università di Pisa, Via Buonarroti, 2 56127 - PISA, Italy (email)
Donato Passaseo - Dipartimento di Matematica, Università di Pisa, Via Buonarroti, 2 56127 - PISA, Italy (email)

Abstract: The paper is concerned with a class of Neumann elliptic problems, in bounded domains, involving the critical Sobolev exponent. Some conditions on the lower order term are given, sufficient to guarantee existence and multiplicity of positive solutions without any geometrical assumption on the boundary of the domain.

Keywords:  Nonlinear elliptic equations, Neumann boundary conditions, positive solutions, critical Sobolev exponent.
Mathematics Subject Classification:  35J65, 35J20, 35J25.

Revised: October 1997;      Published: January 1999.