Existence of continuous eigenvalues for a class of parametric problems involving the (p,2)-laplacian operator

We discuss a parametric eigenvalue problem, where the differential operator is of \((p,2)\)-Laplacian type. We show that, when \(p\neq 2\), the spectrum of the operator is a half line, with the end point formulated in terms of the parameter and the principal eigenvalue of the Laplacian with zero Dirichlet boundary conditions. Two cases are considered corresponding to \(p>2\) and \(p 2\), and to infinity in the case of \(p < 2\).