Shooting method with sign-changing nonlinearity. (February 2015) - Cheng, Ze; Li, Congming
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.