论文标题
不确定sublinear Robin问题的非负解决方案II：本地和全球精确性结果
Nonnegative solutions of an indefinite sublinear Robin problem II: local and global exactness results
论文作者
论文摘要
我们进一步调查了罗宾问题$（p_α）$：$-ΔU= a（x）u^{q} $ in $ω$，$ u \ u \ geq0 $ in $ω$，$ \partial_νu=αu$partial_νu=αu$ on $ \ partialω$;在有限的域上，$ω\ subset \ mathbb {r}^{n} $，带有$ a $ sign-changing和$ 0 <q <1 $。假设存在$α= 0 $的积极解决方案（如果$ Q $足够接近1），我们将$ $α> 0 $的非平底解决方案集的描述（p_α）$锐化。此外，加强对$ a $ a $ a和$ q $的假设，我们提供了全球（即，对于每$α> 0 $）的精确性，结果$（p_α）$的解决方案数量。我们的方法还适用于问题$（s_α）$：$-ΔU=αu + a（x）u^{q} $ in $ω$，$ u \ u \ geq0 $ in $ω$，$ \partial_νu= 0 $ on $ \ \ partialω$。
We go further in the investigation of the Robin problem $(P_α)$: $-Δu=a(x)u^{q}$ in $Ω$, $u\geq0$ in $Ω$, $\partial_νu=αu$ on $\partial Ω$; on a bounded domain $Ω\subset\mathbb{R}^{N}$, with $a$ sign-changing and $0<q<1$. Assuming the existence of a positive solution for $α=0$ (which holds if $q$ is close enough to 1), we sharpen the description of the nontrivial solution set of $(P_α)$ for $α>0$. Moreover, strengthening the assumptions on $a$ and $q$ we provide a global (i.e. for every $α>0$) exactness result on the number of solutions of $(P_α)$ . Our approach also applies to the problem $(S_α)$: $-Δu=αu + a(x)u^{q}$ in $Ω$, $u\geq0$ in $Ω$, $\partial_νu=0$ on $\partial Ω$.
