Electronic Journal of Differential Equations | 卷:2012 |
Existence of bounded positive solutions of a nonlinear differential system | |
关键词: Nonlinear equation; Green's function; asymptotic behavior; singular operator; positive solution; | |
DOI : | |
来源: DOAJ |
【 摘 要 】
In this article, we study the existence and nonexistence of solutions for thesystem$$displaylines{frac{1}{A}(Au')'=pu^{alpha }v^{s}quad hbox{on }(0,infty ), crfrac{1}{B}(Bu')'=qu^{r}v^{eta }quad hbox{on }(0,infty ), crAu'(0)=0,quad u(infty )=a>0, crBv'(0)=0,quad v(infty )=b>0,}$$where $alpha ,eta geq 1$, $s,rgeq 0$, p,q are two nonnegativefunctions on $(0,infty )$ and A, B satisfy appropriate conditions.Using potential theory tools, we show the existence of a positivecontinuous solution. This allows us to prove the existence of entirepositive radial solutions for some elliptic systems.
【 授权许可】
Unknown