| Abstract: |
| \noindent Given $n\in (2,4),$ we study the existence, nonexistence and uniqueness of positive solutions $u \in H_0^1(0,R)$ of
\begin{equation}\label{eq:BBgeneral}
-u``(x)-(n-1)\dfrac{a`(x)}{a(x)}u`(x)= \lambda u(x) + u(x)^p,
\end{equation}
\noindent with boundary condition $u`(0) = u(R) = 0$, under rather general conditions on $a(x)$. Here, as in the original problem, $p=(n+2)/(n-2)$ is the critical Sobolev exponent.
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\noindent
This is a joint work with Rafaael Benguria, PUC, Santiago, Chile. |
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