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 problemsFile | 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.