Existence and Nonexistence of Positive Solutions for Singular p-Laplacian Equation in RN

We study the existence and nonexistence of solutions for the singular quasilinear problem -div(|x|(-ap)|del u|(p-2)del u) = h(x)f(u) + lambda H(x)g(u), x is an element of R-N, u(x) > 0, x is an element of R-N, lim(|x|->infinity) u(x) = 0, where 1 < p < N, 0 <= a < (N - p)/p and f(u) and g(u) behave like u(m) and u(n) with 0 < m <= p - 1 < n at the origin. We obtain the existence by the upper and lower solution method and the nonexistence by the test function method.