Geodesic
Existence of non-negative solutions for predator-prey elliptic systems with a sign-changing nonlinearity
Electronic journal of differential equations, Tome 2011 (2011)
By the method of monotone iteration and Schauder fixed point theorem, we prove the existence of non-negative solutions to the system

$\displaylines{ -\Delta u= \lambda a(x) f(v)\quad \hbox{in }\Omega,\cr -\Delta v= \lambda b(x) g(u)\quad \hbox{in } \Omega,\cr u =v=0\quad \hbox{on }\partial \Omega, }$

for $\lambda$ sufficiently small, where $\Omega$ is a bounded domain in $\mathbb{R}^N$ with smooth boundary $\partial \Omega$ and $\lambda$ is a positive parameter. In this work, we allow the sign changing nature of a and b with $a(x) b(x)\leq 0, \forall x\in \bar{\Omega}$.
Classification : 35J45, 35J55
Keywords: elliptic system, non-negative solution, existence 
@article{EJDE_2011__2011__a99,
     author = {Tyagi,  Jagmohan},
     title = {Existence of non-negative solutions for predator-prey elliptic systems with a sign-changing nonlinearity},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1254.35078},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a99/}
}
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TI  - Existence of non-negative solutions for predator-prey elliptic systems with a sign-changing nonlinearity
JO  - Electronic journal of differential equations
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VL  - 2011
UR  - http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a99/
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%A Tyagi,  Jagmohan
%T Existence of non-negative solutions for predator-prey elliptic systems with a sign-changing nonlinearity
%J Electronic journal of differential equations
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%V 2011
%U http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a99/
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%F EJDE_2011__2011__a99
Tyagi,  Jagmohan. Existence of non-negative solutions for predator-prey elliptic systems with a sign-changing nonlinearity. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a99/