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

Marco Degiovanni, Sergio Lancelotti

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

60 Citazioni (Scopus)

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.
Lingua originaleEnglish
pagine (da-a)907-919
Numero di pagine13
RivistaANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE
Volume24
DOI
Stato di pubblicazionePubblicato - 2007

Keywords

  • Critical point theory
  • Differential equations
  • Equazioni differenziali
  • Teoria dei punti critici

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