Electronic Journal of Differential Equations 15th annual Conference of Applied Mathematics, Univ. of Central Oklahoma,
Electron. J. Diff. Eqns., Conf. 02, 1999, pp. 19-27.

Oscillation of the solution to a singular differential equation

Alexandra Kurepa & Hugh Weithers

Let u be a solution to the initial-value problem
$$u''(t) + {N-1 \over t}u'(t) + u(t) + u(t)|u(t)|^{4/(N-2)}  =  0,
\quad t \in (0,T] $$
$$u(0) =  1/2,\quad u' (0)  =  0\,.$$
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 November 24, 1999.
Subject lassfications: 34B15, 34A10, 35J65.
Key words: critical exponent, singular equation, Sturm comparison theorem.

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Alexandra Kurepa
Department of Mathematics
North Carolina A&T State University
Greensboro, North Carolina 27411 , USA
e-mail: kurepa@ncat.edu
Hugh Weithers
Raytheon AIS, Software Engineer II
e-mail: Weithersho@gvl.esys.com
Tel: 903-457-6048

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