Standing waves for a system of nonlinear Schrödinger equations in RN

Article type: Research Article

Authors: do Ó, João Marcos^{a; *} | Miyagaki, Olímpio H.^b | Santana, Cláudia^c

Affiliations: [a] Department of Mathematics, Federal University of Paraíba, 58059-900 João Pessoa, PB, Brazil | [b] Department of Mathematics, Federal University of Juiz de Fora, 36036-330 Juiz de Fora, MG, Brazil | [c] Department of Exact Sciences and Technology, State University of Santa Cruz, 45662-900 Ilhéus, BA, Brazil

Correspondence: [*] Corresponding author. Tel.: +55 83 3216-7434; Fax: +55 83 3216-7487; E-mail: [email protected].

Abstract: In this paper we study the existence of bound state solutions for stationary Schrödinger systems of the form −Δu+V(x)u=K(x)Fu(u,v)in RN,−Δv+V(x)v=K(x)Fv(u,v)in RN, where N⩾3, V and K are bounded continuous nonnegative functions, and F(u,v) is a C1 and p-homogeneous function with 2<p<2N/(N−2). We give a special attention to the case when V may eventually vanishes. Our arguments are based on penalization techniques, variational methods and Moser iteration scheme.

Keywords: elliptic systems, variational methods, vanishing potential, nonlinear Schrödinger equations, bounded states

DOI: 10.3233/ASY-151347

Journal: Asymptotic Analysis, vol. 96, no. 3-4, pp. 351-372, 2016