Existence of entire solutions for singular quasilinear convective elliptic systems

Abstract

The existence of entire solutions to quasilinear elliptic systems exhibiting both singular and convective reaction terms is discussed. An auxiliary problem, obtained by 'freezing' the convection terms and 'shifting' the singular ones, is first solved. Then, a priori estimates, fixed point arguments, nonlinear regularity, compactness results concerning the gradient terms, besides a regularization-localization procedure, yield the existence of a weak solution to the problem.