Geodesic
Existence of non-negative solutions for predator-prey elliptic systems with a sign-changing nonlinearity
Electronic Journal of Differential Equations, Tome 2011 (2011).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {2011},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a99/}
}
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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/