Existence and multiplicity of weak solutions for a singular quasilinear elliptic equation

摘要

In this paper, we consider the singular quasilinear elliptic equation - div (｜x｜~(-ap)｜Du｜~(p-2)Du) + V(x)｜u｜~(p-2)u = h(x)｜u｜~(q-2)u + λH(x)｜u｜~(r-2)u, x∈R~N{0},(0.1) where λ＞0, -∞＜α＜N-p/p, 1＜p＜N, 1＜q, r < p~* = Np/N-p. The function V(x) is continuous and nonnegative; the functions h(x),H(x)∈ L~∞(B_(R+1) B_τ) with 0＜τ＜R_0＜R＜+∞. Using variational methods, we obtain a number of results on existence and multiplicity of solutions by considering all possible orderings of exponents p,q,r.