Existence and nonexistence of solutions for a quasilinear elliptic system

Qin Li; Zuodong Yang

Qin Li ; Zuodong Yang

Annales Polonici Mathematici, Tome 113 (2015), p. 155-164 / Harvested from The Polish Digital Mathematics Library

Résumé

By a sub-super solution argument, we study the existence of positive solutions for the system ⎧ $- Δ_{p} u = a ₁ (x) F ₁ (x, u, v)$ in Ω, ⎪ $- Δ_{q} v = a ₂ (x) F ₂ (x, u, v)$ in Ω, ⎨u,v > 0 in Ω, ⎩u = v = 0 on ∂Ω, where Ω is a bounded domain in $ℝ^{N}$ with smooth boundary or $Ω = ℝ^{N}$ . A nonexistence result is obtained for radially symmetric solutions.

Publié le : 2015-01-01

Zbl 1326.35151

EUDML-ID : urn:eudml:doc:280748

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     title = {Existence and nonexistence of solutions for a quasilinear elliptic system},
     journal = {Annales Polonici Mathematici},
     volume = {113},
     year = {2015},
     pages = {155-164},
     zbl = {1326.35151},
     language = {en},
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Qin Li; Zuodong Yang. Existence and nonexistence of solutions for a quasilinear elliptic system. Annales Polonici Mathematici, Tome 113 (2015) pp. 155-164. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap113-2-3/