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| POSITIVE PERIODIC SOLUTIONS OF FIRST AND SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS |
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Citation： |
LI Yongxiang.POSITIVE PERIODIC SOLUTIONS OF FIRST AND SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS[J].Chinese Annals of Mathematics B,2004,25(3):413~420 |
| Page view： 1596
Net amount： 761 |
Authors： |
LI Yongxiang; |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10271095), the Gansu
Provincial Natural Science Foundation of China (No.ZS031-A25-003-Z) and the NWNU-KJCXGC-212
Foundation. |
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| Abstract： |
In this paper the existence results of positive $\omega$-periodic
solutions are obtained for second order ordinary differential
equation $-u''(t)=f(t,u(t))\;(t\in {\mathbb R} ),$ and also for
first order ordinary differential equation $u'(t)=f(t,u(t))\;(t\in
{\mathbb R} ),$ where $f:{\mathbb R} \times{\mathbb
R}^+\to{\mathbb R}$ is a continuous function which is
$\omega$-periodic in $t$. The discussion is based on the fixed
point index theory in cones. |
Keywords： |
Positive periodic solution, Cone, Fixed point index |
Classification： |
34C25, 47H10 |
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