Existence of bounded positive solutions of a nonlinear differential system

Electronic Journal of Differential Equations

卷:2012

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