Infinitely many singular radial solutions for quasilinear elliptic systems

Abstract

We prove the existence of infinitely many singular radial positive solutions for a quasilinear elliptic system with no variational structure [Formula: see text] where [Formula: see text] is the unit ball of [Formula: see text] [Formula: see text] [Formula: see text], and [Formula: see text] are non-negative functions. We separate two fundamental classes (the sublinear and superlinear class), and we use respectively the Leray–Schauder Theorem and a method of monotone iterations to obtain the existence of many solutions with a property of singularity around the origin. Finally, we give a sufficient condition for the non-existence.