Existence and nonexistence of solutions for
a quasilinear elliptic system
Annales Polonici Mathematici, Tome 113 (2015) no. 2, pp. 155-164
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
By a sub-super solution argument, we study the existence
of positive solutions for the system
$$\left\{\begin{array}{l@{\quad}l}
-\varDelta_{p}u=a_{1}(x)F_{1}(x,u,v) {\rm in}\ \varOmega,\\
-\varDelta_{q}v=a_{2}(x)F_{2}(x,u,v) {\rm in}\ \varOmega,\\
u,v>0 {\rm in}\ \varOmega,\\
u=v=0 {\rm on}\ \partial\varOmega,\end{array}\right.
$$
where $\varOmega$ is a bounded domain in $\mathbb{R}^{N}$ with smooth boundary or $\varOmega=\mathbb{R}^{N}$. A
nonexistence result is obtained for radially symmetric solutions.
Keywords:
sub super solution argument study existence positive solutions system begin array quad vardelta varomega vardelta varomega varomega partial varomega end array right where varomega bounded domain mathbb smooth boundary varomega mathbb nonexistence result obtained radially symmetric solutions
Affiliations des auteurs :
Qin Li 1 ; Zuodong Yang 2
@article{10_4064_ap113_2_3,
author = {Qin Li and Zuodong Yang},
title = {Existence and nonexistence of solutions for
a quasilinear elliptic system},
journal = {Annales Polonici Mathematici},
pages = {155--164},
year = {2015},
volume = {113},
number = {2},
doi = {10.4064/ap113-2-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap113-2-3/}
}
TY - JOUR AU - Qin Li AU - Zuodong Yang TI - Existence and nonexistence of solutions for a quasilinear elliptic system JO - Annales Polonici Mathematici PY - 2015 SP - 155 EP - 164 VL - 113 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4064/ap113-2-3/ DO - 10.4064/ap113-2-3 LA - en ID - 10_4064_ap113_2_3 ER -
Qin Li; Zuodong Yang. Existence and nonexistence of solutions for a quasilinear elliptic system. Annales Polonici Mathematici, Tome 113 (2015) no. 2, pp. 155-164. doi: 10.4064/ap113-2-3
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