# A nonlinear eigenvalue problem for the periodic scalar p-Laplacian

Roberto Livrea, Giuseppina Barletta, Roberto Livrea, Nikolaos S. Papageorgiou

Risultato della ricerca: Article

5 Citazioni (Scopus)

### Abstract

We study a parametric nonlinear periodic problem driven by the scalar p-Laplacian. We show that if $\hat\lambda_1> 0$ is the first eigenvalue of the periodic scalar p-Laplacian and $\lambda>\hat\lambda_1$, then the problem has at least three nontrivial solutions one positive, one negative and the third nodal. Our approach is variational together with suitable truncation, perturbation and comparison techniques.
Lingua originale English 1075-1086 12 Communications on Pure and Applied Analysis 13 Published - 2014

### Fingerprint

Nonlinear Eigenvalue Problem
P-Laplacian
Scalar
Periodic Problem
First Eigenvalue
Nontrivial Solution
Truncation
Nonlinear Problem
Perturbation

### All Science Journal Classification (ASJC) codes

• Analysis
• Applied Mathematics

### Cita questo

A nonlinear eigenvalue problem for the periodic scalar p-Laplacian. / Livrea, Roberto; Barletta, Giuseppina; Livrea, Roberto; Papageorgiou, Nikolaos S.

In: Communications on Pure and Applied Analysis, Vol. 13, 2014, pag. 1075-1086.

Risultato della ricerca: Article

Livrea, R, Barletta, G, Livrea, R & Papageorgiou, NS 2014, 'A nonlinear eigenvalue problem for the periodic scalar p-Laplacian', Communications on Pure and Applied Analysis, vol. 13, pagg. 1075-1086.
Livrea, Roberto ; Barletta, Giuseppina ; Livrea, Roberto ; Papageorgiou, Nikolaos S. / A nonlinear eigenvalue problem for the periodic scalar p-Laplacian. In: Communications on Pure and Applied Analysis. 2014 ; Vol. 13. pagg. 1075-1086.
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AU - Papageorgiou, Nikolaos S.

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N2 - We study a parametric nonlinear periodic problem driven by the scalar p-Laplacian. We show that if $\hat\lambda_1> 0$ is the first eigenvalue of the periodic scalar p-Laplacian and $\lambda>\hat\lambda_1$, then the problem has at least three nontrivial solutions one positive, one negative and the third nodal. Our approach is variational together with suitable truncation, perturbation and comparison techniques.

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KW - Analysis

KW - Applied Mathematics

KW - Constant sign and nodal solutions

KW - Extremal solutions

KW - Parametric equation

KW - Second deformation theorem

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