In this paper the existence of a nontrivial solution to a parametric Neumann problem for a class of nonlinear elliptic equations involving the p(x)-Laplacian and a discontinuous nonlinear term is established. Under a suitable condition on the behavior of the potential at 0+, we obtain an interval ]0, λ∗], such that, for any λ ∈ ]0, λ∗] our problem admits at least one nontrivial weak solution. The solution is obtained as a critical point of a locally Lipschitz functional. In addition to providing a new conclusion on the existence of a solution even for λ = λ∗, our theorem also includes other results in the literature for regular problems

Existence results for a Neumann problem involving the p(x)-Laplacian with discontinuous nonlinearities

CHINNI', Antonia
Secondo
;
2016-01-01

Abstract

In this paper the existence of a nontrivial solution to a parametric Neumann problem for a class of nonlinear elliptic equations involving the p(x)-Laplacian and a discontinuous nonlinear term is established. Under a suitable condition on the behavior of the potential at 0+, we obtain an interval ]0, λ∗], such that, for any λ ∈ ]0, λ∗] our problem admits at least one nontrivial weak solution. The solution is obtained as a critical point of a locally Lipschitz functional. In addition to providing a new conclusion on the existence of a solution even for λ = λ∗, our theorem also includes other results in the literature for regular problems
File in questo prodotto:
File Dimensione Formato  
Neumann p(x) discontinuous.pdf

solo gestori archivio

Descrizione: articolo principale
Tipologia: Versione Editoriale (PDF)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 694.99 kB
Formato Adobe PDF
694.99 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3061591
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 22
  • ???jsp.display-item.citation.isi??? 20
social impact