论文标题
关于环形中半线性方程的溶液的唯一性
On the uniqueness of solutions of a semilinear equation in an annulus
论文作者
论文摘要
我们确定了阳性径向解决方案的独特性 $$ \ begin {case}ΔU +f（u）= 0，\ quad x \ in \\ u（x）= 0 \ quad x \ in \ partial a \ end {cases} $$其中$ a：= a_ {a，b} = \ {x \ in {\ mathbb r}^n：a <| x | x | <b \} $，$ 0 <a <a <a <b \ le \ le \ infty $。 我们假设c [0，\ infty）\ cap c^1（0，\ infty）$的非线性$ f \是如此，以至于$ f（0）= 0 $且满足某些凸度和增长条件，并且$ f（s）> 0 $要么$ s> 0 $，或者在$ b> 0 $中，$ b> 0 $ as $ as $ and $ and in in IS $ and in in in IS in in in IS in in in in IS in IS in IS 0 $ 0，0 in in IS 0 in in in IS in IS in IS in IS in IS $ 0。 $（b，\ iffty）$。
We establish the uniqueness of positive radial solutions of $$\begin{cases} Δu +f(u)=0,\quad x\in A \\ u(x) =0 \quad x\in \partial A \end{cases} $$ where $A:=A_{a,b}=\{ x\in {\mathbb R}^n : a<|x|<b \}$, $0<a<b\le\infty$. We assume that the nonlinearity $f\in C[0,\infty)\cap C^1(0,\infty)$ is such that $f(0)=0$ and satisfies some convexity and growth conditions, and either $f(s)>0$ for all $s>0$, or has one zero at $B>0$, is non positive and not identically 0 in $(0,B)$ and it is positive in $(B,\infty)$.
