Continuous spectrum for a two phase eigenvalue problem with an indefinite and unbounded potential

Calogero Vetro; Francesca Vetro; Nikolaos S. Papageorgiou

Continuous spectrum for a two phase eigenvalue problem with an indefinite and unbounded potential

Calogero Vetro, Francesca Vetro, Nikolaos S. Papageorgiou

Matematica e Informatica

Risultato della ricerca: Article

Abstract

We consider a two phase eigenvalue problem driven by the (p,q)-Laplacian plus an indefinite and unbounded potential, and Robin boundary condition. Using a modification of the Nehari manifold method, we show that there exists a nontrivial open interval I⊆R such that every λ∈I is an eigenvalue with positive eigenfunctions. When we impose additional regularity conditions on the potential function and the boundary coefficient, we show that we have smooth eigenfunctions.

Lingua originale	English
pagine (da-a)	4102-4118
Numero di pagine	17
Rivista	Journal of Differential Equations
Volume	268
Stato di pubblicazione	Published - 2020

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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Vetro, C., Vetro, F., & Papageorgiou, N. S. (2020). Continuous spectrum for a two phase eigenvalue problem with an indefinite and unbounded potential. Journal of Differential Equations, 268, 4102-4118.

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abstract = "We consider a two phase eigenvalue problem driven by the (p,q)-Laplacian plus an indefinite and unbounded potential, and Robin boundary condition. Using a modification of the Nehari manifold method, we show that there exists a nontrivial open interval I⊆R such that every λ∈I is an eigenvalue with positive eigenfunctions. When we impose additional regularity conditions on the potential function and the boundary coefficient, we show that we have smooth eigenfunctions.",

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T1 - Continuous spectrum for a two phase eigenvalue problem with an indefinite and unbounded potential

AU - Vetro, Calogero

AU - Vetro, Francesca

AU - Papageorgiou, Nikolaos S.

PY - 2020

Y1 - 2020

N2 - We consider a two phase eigenvalue problem driven by the (p,q)-Laplacian plus an indefinite and unbounded potential, and Robin boundary condition. Using a modification of the Nehari manifold method, we show that there exists a nontrivial open interval I⊆R such that every λ∈I is an eigenvalue with positive eigenfunctions. When we impose additional regularity conditions on the potential function and the boundary coefficient, we show that we have smooth eigenfunctions.

AB - We consider a two phase eigenvalue problem driven by the (p,q)-Laplacian plus an indefinite and unbounded potential, and Robin boundary condition. Using a modification of the Nehari manifold method, we show that there exists a nontrivial open interval I⊆R such that every λ∈I is an eigenvalue with positive eigenfunctions. When we impose additional regularity conditions on the potential function and the boundary coefficient, we show that we have smooth eigenfunctions.

UR - http://hdl.handle.net/10447/398444

UR - https://doi.org/10.1016/j.jde.2019.10.026

M3 - Article

VL - 268

SP - 4102

EP - 4118

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

ER -