Global Solutions of Nonlinear Initial Value Problems
by
John V. Baxley
Wake Forest University, NC
Coauthors: Cynthia G. Enloe

We study the initial value problem

1 m(t) (p(t)y')'+ f(t, y, p(t)y) = 0 ,     t > 0 ,

y(0)=A,     lim t --> 0+  p(t) y'(t) = B.

We allow a singularity at t=0, so y'(t) may not be bounded near t=0. We provide conditions sufficient to give existence of a solution for all t > 0 for any pair A, B; our conditions are rather mild and such a solution may grow exponentially, or worse, for t large.

Date received: March 12, 2003