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EnglishWe 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.
Papageorgiou N.S., Vetro C., & Vetro F. (2020). Continuous spectrum for a two phase eigenvalue problem with an indefinite and unbounded potential. JOURNAL OF DIFFERENTIAL EQUATIONS, 268(8), 4102-4118.
| Data di pubblicazione: | 2020 |
| Titolo: | Continuous spectrum for a two phase eigenvalue problem with an indefinite and unbounded potential |
| Autori: | |
| Citazione: | Papageorgiou N.S., Vetro C., & Vetro F. (2020). Continuous spectrum for a two phase eigenvalue problem with an indefinite and unbounded potential. JOURNAL OF DIFFERENTIAL EQUATIONS, 268(8), 4102-4118. |
| Rivista: | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jde.2019.10.026 |
| 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. |
| URL: | https://doi.org/10.1016/j.jde.2019.10.026 |
| Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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http://hdl.handle.net/10447/398444
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