Ground state solutions to nonlinear equations with p-Laplacian. (July 2019)

• Record Type: Journal Article
• Authors: Došlá, Zuzana; Matucci, Serena
• Is Part Of: Nonlinear analysis. Volume 184(2019)
• Page Start: 1
• Page End: 16
• Publication Date: 2019-07
• Subjects: 34B40 -- 34B18; Second order nonlinear differential equation -- Ground state solution -- Boundary value problem on the half-line; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.01.032
• Languages: English
• ISSNs: 0362-546X

Abstract

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.