Nonlinear initial-value problems with positive global solutions

• Main Authors: John V. Baxley, Cynthia G. Enloe
• Format: Article
• Language: English
• Published: Texas State University 2003-02-01
• Series: Electronic Journal of Differential Equations
• Subjects: Nonlinear initial-value problems; positive global solutions; Caratheodory.
• Online Access: http://ejde.math.txstate.edu/conf-proc/10/b1/abstr.html

We give conditions on $m(t)$, $p(t)$, and $f(t,y,z)$ so that the nonlinear initial-value problem {gather*} frac{1}{m(t)} (p(t)y')' + f(t,y,p(t)y') = 0,quadmbox{for }t>0, y(0)=0,quad lim_{t o 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 $t=0$.