Ground state solutions to nonlinear equations with p-Laplacian

The existence of positive radial solutions is investigated for a nonlinear elliptic equation with p-Laplace operator and sign-changing weight, both in superlinear and sublinear case. We 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'(R) = 0 and tends to zero at infinity. Our method is based on a fixed point result for boundary value problems on noncompact intervals and on asymptotic properties of suitable auxiliary half-linear differential equations. The results are new also for the classical Laplace operator and may be used for proving the existence of ground state solutions and decaying solutions with exactly k-zeros which are defined in all the space. Some examples illustrate our results.