Electronic Journal of Differential Equations,
Conf. 10 (2002), pp. 71-78.
Title: Nonlinear initial-value problems with positive global solutions
Authors: John V. Baxley (Wake Forest Univ., Winston-Salem, NC, USA)
Cynthia G. Enloe (Wake Forest Univ., Winston-Salem, NC, USA)
Abstract:
We give conditions on $m(t)$, $p(t)$, and
$f(t,y,z)$ so that the nonlinear initial-value problem
\begin{gather*}
\frac{1}{m(t)} (p(t)y')' + f(t,y,p(t)y') = 0,\quad\mbox{for }t>0,\\
y(0)=0,\quad \lim_{t \to 0^+} p(t)y'(t) = B,
\end{gather*}
has at least one positive solution for all $t>0$,
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.
Math Subject Classifications: 34A12, 34B15.
Key Words: Nonlinear initial-value problems; positive global solutions; Caratheodory.