We prove non-existence and existence of entire positive solutions for a Schrödinger quasilinear elliptic system. To prove the non-existence, we combine a carefully-chosen test function with some results that we proved concerning the positivity of a kind of principal eigenvalue of a eigenvalue problem in RN with indefinite weights. Contrary to the existence, the non-existence results for this cl...

Abstract In this article, our aim is to establish a generalized version of Lions-type theorem for the p -Laplacian. As an application theorem, we consider existence ground state solution quasilinear elliptic equation with critical growth.

Karátson and Korotov developed a sharp upper global a posteriori error estimator for a large class of nonlinear problems of elliptic type, see J.Karátson, S.Korotov (2009). The goal of this paper is to check its numerical performance, and to demonstrate the efficiency and accuracy of this estimator on the base of quasilinear elliptic equations of the second order. The focus will be on the techn...