We prove that the quasilinear equation -\Delta_p u=\lambda V |u|^{p-2}u+g(x,u), with g subcritical and p-superlinear at 0 and at infinity, admits a nontrivial weak solution u in W^{1,p}_0(\Omega) for any \lambda in R. A minimax approach, allowing also an estimate of the corresponding critical level, is used. New linking structures, associated to certain variational eigenvalues of -\Delta_p u=\lambda V |u|^{p-2}u, are recognized, even in absence of any direct sum decomposition of W^{1,p}_0(\Omega) related to the eigenvalue itself.
Degiovanni, M., Lancelotti, S., Linking over cones and nontrivial solutions for p-Laplace equations with p-superlinear nonlinearity, <<ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE>>, 2007; 24 (6): 907-919. [doi:10.1016/j.anihpc.2006.06.007] [http://hdl.handle.net/10807/3284]
Linking over cones and nontrivial solutions for p-Laplace equations with p-superlinear nonlinearity
Degiovanni, Marco;Lancelotti, Sergio
2007
Abstract
We prove that the quasilinear equation -\Delta_p u=\lambda V |u|^{p-2}u+g(x,u), with g subcritical and p-superlinear at 0 and at infinity, admits a nontrivial weak solution u in W^{1,p}_0(\Omega) for any \lambda in R. A minimax approach, allowing also an estimate of the corresponding critical level, is used. New linking structures, associated to certain variational eigenvalues of -\Delta_p u=\lambda V |u|^{p-2}u, are recognized, even in absence of any direct sum decomposition of W^{1,p}_0(\Omega) related to the eigenvalue itself.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.