Bounded positive entire solutions of singular quasilinear elliptic equations

Suppose that β⩾0β⩾0 is a constant and that f:RN×R+×RN→R is a continuous function with R+:=(0,∞)R+:=(0,∞). This paper investigates N-dimensional singular, quasilinear elliptic equations of the formΔu+f(x,u,∇u)u−β=0,x∈RN(N⩾3) and gives some sufficient conditions for the equations to have (i) a decaying positive entire solution or (ii) infinitely many positive entire solutions each of which is bounded with a positive lower-bound.