Ground state solutions are solutions \( u \) of some kind of equations such as the equation \[ \operatorname{div} (r(x)\left|\nabla u\right|^{p-2}\nabla u )+ q(x) F(u) = 0, p > 1,x\in \mathbb{R}^d, \] which are positive, minimize a certain energy functional, and satisfy \(\lim_{|x|\to\infty} u(x) = 0.\) In this paper the authors investigate the existence of positive radial solutions for the following nonlinear elliptic equation with \(p\)-Laplace operator and sign-changing weight \[ (a(t)\Phi(x^\prime ))^\prime + b(t)F(x) = 0, t \in [t_0, \infty), t_0 \geq 0, \] where \( \Phi(u) = \left| u\right|^{\alpha-1}u = \left| u \right|^\alpha\operatorname{sgn} u, \alpha = p - 1> 0 \). They use a fixed point result for boundary value problems on noncompact intervals and on asymptotic properties of suitable auxiliary half-linear differential equations to prove the existence of solutions \(u,\) which are globally defined and positive outside a ball of radius \(r\), satisfy fixed initial conditions \(u(r) = c > 0, u^{\prime} (r) = 0 \) and tend to zero at infinity.