Existence and Asymptotic Behavior of Singular Solutions of Quasilinear Elliptic Equations in R~n

摘要

In this paper we consider the quasilinear elliptic equation (1) div(|▽u|~(m-1)▽u) + f(u) = 0 where n > m > 1. We obtain a necessary and sufficient condition for the existence of positive radial solutionsons u = u(r) on [r_0, ∞], where r_0 > 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.