The Existence and Uniqueness of a Positive Solution of an Elliptic System

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Volume 17, Issue 1

Joon Hyuk Kang & Yun Myung Oh

J. Part. Diff. Eq., 17 (2004), pp. 29-48.

Published online: 2004-02

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Abstract

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.

Keywords

Lotka-Volterra competition model coexistence state

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@Article{JPDE-17-29, author = {}, title = {The Existence and Uniqueness of a Positive Solution of an Elliptic System}, journal = {Journal of Partial Differential Equations}, year = {2004}, volume = {17}, number = {1}, pages = {29--48}, abstract = { 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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5374.html} }

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.

Joon Hyuk Kang & Yun Myung Oh . (2019). The Existence and Uniqueness of a Positive Solution of an Elliptic System. Journal of Partial Differential Equations. 17 (1). 29-48. doi:

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