Fifth Mississippi State Conference on Differential Equations and Computational Simulations,
Electron. J. Diff. Eqns., Conf. 10, 2003, pp. 71-78.

Nonlinear initial-value problems with positive global solutions

John V. Baxley & Cynthia G. Enloe

Abstract:
We give conditions on $m(t)$, $p(t)$, and $f(t,y,z)$ so that the nonlinear initial-value problem
$$\displaylines{ \frac{1}{m(t)} (p(t)y')' + f(t,y,p(t)y') = 0, \quad\hbox{for }t greater than 0,\cr y(0)=0,\quad \lim_{t \to 0^+} p(t)y'(t) = B, }$$
has at least one positive solution for all $t greater than 0$, when $B$ is a sufficiently small positive constant. We allow a singularity at $t=0$ so the solution $y'(t)$ may be unbounded near $t=0$.

Published February 28, 2003.
Subject classifications: 34A12, 34B15.
Key words: Nonlinear initial-value problems, positive global solutions, Caratheodory.

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John V. Baxley
Department of Mathematics
Wake Forest University
Winston-Salem, NC 27109, USA
e-mail: baxley@mthcsc.wfu.edu
Cynthia G. Enloe
Department of Mathematics
Wake Forest University
Winston-Salem, NC 27109, USA

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