Necessary and Sufficient Conditions of Existence for Positive Solution to a Class of Quasilinear Elliptic Systems in R N

Abstract

In this paper, we establish the necessary and sufficient conditions of existence for a positive solution to a class of non-variational quasilinear elliptic systems in R N . The sufficient condition of existence result bases on the Mountain Pass Lemma and the sub-super solution methods, and the necessary condition is a consequence of a Picone’s identity. The system models some phenomena in different physical and other natural sciences: non-Newtonian mechanics, nonlinear elasticity and glaciology, combustion theory, population biology and so on.