Indefinite perturbations of an unbalanced growth eigenvalue problem

Abstract

We consider indefinite perturbations of a double-phase eigenvalue problem. The perturbation is sublinear or superlinear, and it is in general sign-changing. Using the Nehari manifold, we prove the existence of two constant sign solutions for both cases (sublinear and superlinear), when the parameter $\lambda \in (0,{\hat{\lambda }}_1^{\alpha })$ with ${\hat{\lambda }}_1^{\alpha }>0$ being the principal eigenvalue of Dirichlet weighted $p$-Laplace operator $-{\Delta }_p^{\alpha }$.