Nonlinear initial-value problems with positive global solutions
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 $t>0$,...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2003-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/conf-proc/10/b1/abstr.html |
| Summary: | 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 $t=0$. |
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| ISSN: | 1072-6691 |