Artículos de revistas
A relation between the domain topology and the number of minimal nodal solutions for a quasilinear elliptic problem
Registro en:
Nonlinear Analysis-theory Methods & Applications. Pergamon-elsevier Science Ltd, v. 62, n. 4, n. 615, n. 628, 2005.
0362-546X
WOS:000230635400003
10.1016/j.na.2005.03.073
Autor
Furtado, MF
Institución
Resumen
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. 62 4 615 628