Shooting method with sign-changing nonlinearity. (February 2015)

• Record Type: Journal Article
• Authors: Cheng, Ze; Li, Congming
• Is Part Of: Nonlinear analysis. Volume 114(2015)
• Page Start: 2
• Page End: 12
• Publication Date: 2015-02
• Subjects: 35B09 -- 35B33 -- 35J30 -- 35J48 -- 53A30 -- 34A34; Existence of solution -- Degree theory -- Shooting method -- Rellich–Pohožaev identity; 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.2014.10.019
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study the existence of solution to a nonlinear system: (0.1) { − Δ u i = f i ( u ) in R n, u i > 0 in R n, i = 1, 2, …, L for sign changing nonlinearities f i 's. A degree theory approach to shooting method for this type of problems is introduced independently by Li (2013) and Liu et al. (2006) for nonnegative f i 's. However, many systems of nonlinear Schödinger type involve interaction with undetermined sign. Here, based on some new dynamic estimates, we are able to extend the degree theory approach to systems with sign-changing source terms.