6533b853fe1ef96bd12acc7f

RESEARCH PRODUCT

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

Nikolaos S. PapageorgiouFrancesca VetroCalogero Vetro

subject

Indefinite unbounded potentialPure mathematicsNehari manifoldApplied Mathematics010102 general mathematicsContinuous spectrumBoundary (topology)Function (mathematics)Robin boundary conditionMathematics::Spectral TheoryEigenfunction01 natural sciences(pq)-LaplacianRobin boundary condition010101 applied mathematicsSettore MAT/05 - Analisi MatematicaLagrange multiplier rule0101 mathematicsSobolev embedding theoremNehari manifoldLaplace operatorAnalysisEigenvalues and eigenvectorsMathematics

description

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.

yearjournalcountryeditionlanguage
2020-04-01Journal of Differential Equations
https://doi.org/10.1016/j.jde.2019.10.026