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|Type:||Artigo de periódico|
|Title:||A relation between the domain topology and the number of minimal nodal solutions for a quasilinear elliptic problem|
|Abstract:||We consider the quasilinear problem -div(vertical bar del u vertical bar(p-2)del u) + vertical bar u vertical bar(p-2)u = vertical bar u vertical bar(q-2)u in Omega, u = 0 on partial derivative Omega where Q subset of R-N is a bounded smooth domain, 1 < p < N and p < q < p* = Np/(N - p). We show that if Omega is invariant by a non-trivial orthogonal involution then, for q close to p*, the equivariant topology of Omega is related with the number of solutions which change sign exactly once. The results complement those of Castro and Clapp [Nonlinearity 16 (2003) 579-590] since we consider subcritical nonlinearities and the quasilinear case. Without any assumption of symmetry we also extend Theorem B in Benci and Cerami [Arch. Rational. Mech. Anal. 114 (1991) 79-93] for the quasilinear case and prove that the topology of Omega affects the number of positive solutions. (c) 2005 Elsevier Ltd. All rights reserved.|
|Editor:||Pergamon-elsevier Science Ltd|
|Appears in Collections:||Artigos e Materiais de Revistas Científicas - Unicamp|
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