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

We study initial value problems of the form

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, and so y'(t) may not be bounded near t=0, although we require that y be continuous at t=0. The singularity may be caused by the behaviour of m or p or f near t=0, or by some combination of them. We provide conditions on these functions which guarantee the existence of a (possibly non-unique) solution existing globally on 0 < t < ∞, and such a solution may grow exponentially or worse.

Date received: March 30, 2007