Asymptotic behavior of ground state solutions for sublinear and singular nonlinear Dirichlet problems

Electronic Journal of Differential Equations

关键词: Asymptotic behavior;    Dirichlet problem;    ground sate solution;    singular equations;    sublinear equations;   

DOI  :  

来源: DOAJ

【 摘 要 】

In this article, we are concerned with the asymptotic behaviorof the classical solution to the semilinear boundary-valueproblem$$Delta u+a(x)u^{sigma }=0$$in $mathbb{R}^n$, $u>0$, $lim_{|x|o infty }u(x)=0$,where $sigma <1$. The special feature is to consider thefunction $a$ in $C_{m loc}^{alpha }(mathbb{R}^n)$,$00$ satisfying$$frac{1}{c}frac{L(|x| +1)}{(1+|x| )^{lambda }}leq a(x)leq cfrac{L(|x| +1)}{(1+|x| )^{lambda }},$$where $L(t):=exp ig(int_1^tfrac{z(s)}{s}dsig)$,with $zin C([1,infty ))$ such that $lim_{to infty } z(t)=0$.The comparable asymptotic rate of $a(x)$ determines the asymptoticbehavior of the solution.

【 授权许可】

Unknown