صندلی اداری

NOTE ON EXISTENCE OF POSITIVE SOLUTIONS FOR ELLIPTIC EQUATIONS

Chien-Hsiung Lin

Abstract


In this article, we shall prove that under suitable conditions on $f(r,u)$,
the boundary value problem
\[
\begin{array}{ll}
\left \{
\begin{array}{lll}
&(E_{\lambda^*})\quad (r^{n-1}w')'+\lambda f(r,w)=0,~~~0<r<1,\\
&(BC^*)\quad w(0)=w(1)=0,
\end{array}
\right.
\end{array}
\eqno{(P_{\lambda})}
\]
has a critical value $\lambda^*$, that is, $(P_{\lambda})$ has a positive solution for $0<\lambda <\lambda^*$
and has no positive solution for $\lambda >\lambda^*.$

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