Least energy radial sign-changing solution for the Schrodinger-Poisson system in R-3 under an asymptotically cubic nonlinearity

Author(s)

Gonzalo Murcia, Edwin ^[1] ; Siciliano, Gaetano ^[2]

Affiliation

^[1] Pontificia Univ Javeriana, Dept Matemat, Carrera 7 43-82, Bogota - Colombia

^[2] Univ Sao Paulo, Inst Matemat & Estat, Dept Matemat, Rua Matao 1010, BR-05508090 Sao Paulo - Brazil

• Document type: Journal article
• Source: Journal of Mathematical Analysis and Applications; v. 474, n. 1, p. 544-571, JUN 1 2019.
• Web of Science Citations: 1

Abstract

In this paper we consider the following Schrodinger-Poisson system in the whole R-3, [-Delta u + u + lambda phi u = f (u) in R-3, -Delta phi = u(2) in R-3, where lambda > 0 and the nonlinearity f is ``asymptotically cubic{''} at infinity. This implies that the nonlocal term phi u and the nonlinear term f(u) are, in some sense, in a strict competition. We show that the system admits a least energy sign-changing and radial solution obtained by minimizing the energy functional on the so-called modal Nehari set. (C) 2019 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 18/17264-4 - Existence of solutions for nonlinear elliptic equations
• Grantee: Gaetano Siciliano
• Support Opportunities: Regular Research Grants