On the Existence of Positive Eigenvalues for Linear and Nonlinear Equations with Indefinite Weight

We prove the existence of positive eigenvalues for two types of equations having an indefinite weight. We consider the linear case, and we show the existence of a positive principal eigenvalue corresponding to a positive eigenfunction. For the nonlinear case, we show that the set of positive eigenvalues is an unbounded interval, and that the corresponding eigenfunctions are positive.

Keywords:

• Indefinite Weight
• Kato-class
• Superharmonic Function
• Principal Eigenvalue
• Eigenfunction