Geodesic
Existence of solutions for a sublinear system of elliptic equations
Electronic Journal of Differential Equations, Tome 2000 (2000).

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

Summary: We study the existence of non-trivial non-negative solutions for the system $$ \displaylines{ -\Delta u = |x|^av^p \cr \Delta v = |x|^bu^q\,, }$$ where $p$ and $q$ are positive constants with $pq 1$, and the domain is the unit ball of ${\Bbb R}^N$ (N greater than 2) except for the center zero. We look for pairs of functions that satisfy the above system and Dirichlet boundary conditions set to zero. Our results also apply to some super-linear systems.
Classification : 35A20, 35J60, 34B18
Keywords: semilinear elliptic systems, sub-harmonic functions 
@article{EJDE_2000__2000__a3,
     author = {Cid, Carlos and Yarur, Cecilia},
     title = {Existence of solutions for a sublinear system of elliptic equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2000},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a3/}
}
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Cid, Carlos; Yarur, Cecilia. Existence of solutions for a sublinear system of elliptic equations. Electronic Journal of Differential Equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a3/