Existence and nonexistence of radial positive solutions of superlinear elliptic systems.
Ahammou, Abdelaziz
Publicacions Matemàtiques, Tome 45 (2001), p. 399-419 / Harvested from Biblioteca Digital de Matemáticas
Access to full text

The main goal in this paper is to prove the existence of radial positive solutions of the quasilinear elliptic system

⎧ -Δpu = f(x,u,v) in Ω,

⎨ -Δqv = g(x,u,v) in Ω,

⎩ u = v = 0 on ∂Ω,

where Ω is a ball in RN and f, g are positive continuous functions satisfying f(x, 0, 0) = g(x, 0, 0) = 0 and some growth conditions which correspond, roughly speaking, to superlinear problems. Two different sets of conditions, called strongly and weakly coupled, are given in order to obtain existence. We use the topological degree theory combined with the blow up method of Gidas and Spruck. When Ω = RN, we give some sufficient conditions of nonexistence of radial positive solutions for Liouville systems.

Publié le : 2001-01-01
DMLE-ID : 3956 
@article{urn:eudml:doc:41435,
     title = {Existence and nonexistence of radial positive solutions of superlinear elliptic systems.},
     journal = {Publicacions Matem\`atiques},
     volume = {45},
     year = {2001},
     pages = {399-419},
     mrnumber = {MR1876914},
     zbl = {1034.35040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41435}
}

Ahammou, Abdelaziz. Existence and nonexistence of radial positive solutions of superlinear elliptic systems.. Publicacions Matemàtiques, Tome 45 (2001) pp. 399-419. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41435/