Geodesic
A predator-prey model with combined death and competition terms
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 1, pp. 283-295

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The existence of a positive solution for the generalized predator-prey model for two species $$ \begin{gathered} \Delta u + u(a + g(u,v)) = 0\quad \mbox {in}\ \Omega ,\\ \Delta v + v(d + h(u,v)) = 0\quad \mbox {in} \ \Omega ,\\ u = v = 0\quad \mbox {on}\ \partial \Omega , \end{gathered} $$ are investigated. The techniques used in the paper are the elliptic theory, upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties of the solution of logistic equations.
Classification : 35J47, 35J57, 35Q92, 92D25
Keywords: predator-prey model; coexistence state 
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     author = {Kang, Joon Hyuk and Lee, Jungho},
     title = {A predator-prey model with combined death and competition terms},
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     pages = {283--295},
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     volume = {60},
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     zbl = {1224.35100},
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Kang, Joon Hyuk; Lee, Jungho. A predator-prey model with combined death and competition terms. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 1, pp. 283-295. http://geodesic.mathdoc.fr/item/CMJ_2010__60_1_a22/