Ground state solutions to nonlinear equations with p-Laplacian. (July 2019) - Došlá, Zuzana; Matucci, Serena
Abstract: We investigate the existence of positive radial solutions 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 tend 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 the whole space. Some examples illustrate our results.