论文标题
半线性Ornstein-Uhlenbeck方程的最佳liouville定理
Optimal Liouville theorem for a semilinear Ornstein-Uhlenbeck equation
论文作者
论文摘要
半线性Ornstein-uhlenbeck方程的解决方案的琐事问题，\ [ΔW-\ frac {1} {2} {2} {2} \ langle x，\ nabla w \ nabla w \ rangle- \ rangle- \fracλ{p-1}据表明，如果$ p> 1 $是sobolev sibegition subclitical或crigical，并且$λ\ leq 1 $，则所有有限的整个解决方案都是恒定的。此外，在关键情况下，径向解决方案的子类中也存在相同的结论。
The question of triviality of solutions of the semilinear Ornstein-Uhlenbeck equation, \[ Δw-\frac{1}{2} \langle x,\nabla w\rangle-\fracλ{p-1}w+|w|^{p-1}w=0, \] is considered. It is shown, that if $p>1$ is Sobolev subcritical or critical and $λ\leq 1$, then all bounded entire solutions are constant. Moreover, in the critical case, the same conclusion holds in the subclass of radial solutions provided that $n\geq 4$ and $λ\in \left[\frac{3 n}{2(n-1)},2\right]$.
