Principal eigenvalues for some quasilinear elliptic equations onRn

We improve some previous results for the principal eigenvalue of the p-laplacian defined on IRN, study regularity of the corresponding eigenfunctions and give an existence result of the type below the first eigenvalue (or between the first eigenvalues) for a certain perturbed problem. Based in our approach for the equation we deduce existence, ∗Key Phrases: p-Laplacian systems, nonlinear eigenvalues problems, indefinite weight, homogenious Sobolev Spaces, unbounded domain, perturbation, maximum principle