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.
|Number of pages||17|
|Journal||Journal of Differential Equations|
|Publication status||Published - 2020|
All Science Journal Classification (ASJC) codes
- Applied Mathematics
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.