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.

Linking over cones and nontrivial solutions for p-Laplace equations with p-superlinear nonlinearity / Lancelotti, Sergio; Degiovanni, M.. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 24:6(2007), pp. 907-919. [10.1016/j.anihpc.2006.06.007]

Linking over cones and nontrivial solutions for p-Laplace equations with p-superlinear nonlinearity

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/1447682
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