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

Calogero Vetro, Francesca Vetro, Nikolaos S. Papageorgiou

Research output: Contribution to journalArticle


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.
Original languageEnglish
Pages (from-to)4102-4118
Number of pages17
JournalJournal of Differential Equations
Publication statusPublished - 2020


All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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