Infinitely many singular radial solutions for quasilinear elliptic systems

We prove the existence of infinitely many singular radial positive solutions for a quasi-linear elliptic system with no variational structure {-Delta(P)mu = f(x ,nu) in B' Delta(q)nu = f(x ,nu) in B' u = nu = 0 on (sic)B } where B is the unit ball of R-N, N > 1, B' = B\{0}, and f, g 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.