Existence and asymptotic behavior of singular solutions of quasilinear elliptic equations in Rⁿ

In this paper we consider the quasilinear elliptic equation (1) div(|∇u|^m-2∇u) + f(u) = 0 where n > m > 1. We obtain a necessary and sufficient condition for the existence of positive radial solutions u = u(r) on [r₀, ∞), where r₀ > 0. If f satisfies a further condition, then Eq. (1) possesses infinitely many singular ground state solutions u(r) satisfying u(r) ∼ r^-(n-m)/m-1 at ∞ and u(r) → ∞ as r → 0⁺. We also obtain some important conclusions via our main results.