Existence of radial solutions for the \(p\)-Laplacian elliptic equations with weights (Q874700)

The authors consider singular quasilinear elliptic equations of the form \[ \text{div} (g(| x| ) | Du| ^{p-2} Du) + h(| x| )f(u)=0,\;\;\; \text{in}\;\; \mathbb{R}^N, \] where \(p>1\), \(N \geq 1\), \(g,\, h: \mathbb{R}^+ \to \mathbb{R}^+\), \(Du = (\partial u / \partial x_1, \ldots \partial u / \partial x_N)\) and \(f <0\) near \(u=0\). Under certain conditions they prove the existence (as well as nonexistence) of non trivial radial solutions, which tend to zero at infinity.