TY - JOUR
T1 - The Existence and Uniqueness of a Positive Solution of an Elliptic System
JO - Journal of Partial Differential Equations
VL - 1
SP - 29
EP - 48
PY - 2004
DA - 2004/02
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5374.html
KW - Lotka-Volterra competition model
KW - coexistence state
AB -  The existence and uniqueness of the positive solution for the generalized Lotka-Volterra competition model for several competing species Δu^i + u^i(a - g(u¹, ..., uN^)) = 0 in Ω , u^i = 0 on ∂Ω , for i = 1, ...,N were investigated. The techniques used in this paper are elliptic theory, upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations.