Electronic Journal of Differential Equations,
Conference 02 (1999), pp. 19--27.

Title: Oscillation of the solution to a singular differential equation

Authors: Alexandra Kurepa (North Carolina A&T State Univ. Greensboro, USA)
 Hugh Weithers (North Carolina A&T State Univ. Greensboro, USA) 
 
Abstract: 
Let $u$ be a solution to the initial-value problem
\begin{eqnarray*}
&u''(t) + \frac{N-1}{t}u'(t) + u(t) + u(t)|u(t)|^{4/(N-2)}  =  0,
\quad t \in (0,T]& \\
&u(0) =  \frac {1}{2},\quad u' (0)  =  0\,. &
\end{eqnarray*}
In this paper we show that if $N \leq 6$, then the distance between the two
consecutive zeroes of $u$ is ``close" to $\pi$.  The proof is based
on an energy analysis and the Sturm comparison theorem.


Published December 24, 1999.
Math Subject Classifications: 34B15, 34A10, 35J65.
Key Words: Critical exponent; singular equation; Sturm comparison theorem.