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.

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 [10.1016/j.jde.2019.10.026].

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

Vetro C.;
2020-01-01

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.
Settore MAT/05 - Analisi Matematica
https://doi.org/10.1016/j.jde.2019.10.026
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 [10.1016/j.jde.2019.10.026].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/398444
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