|
|
| |
| Resonance Problem for a Class of Duffing’s Equations |
| |
Citation： |
Ding Tongren,Ding Weiyue.Resonance Problem for a Class of Duffing’s Equations[J].Chinese Annals of Mathematics B,1985,6(4):427~432 |
| Page view： 903
Net amount： 957 |
Authors： |
Ding Tongren; Ding Weiyue |
|
|
| Abstract： |
Consider the Duffing's equation
$\ddot x+g(x)=f(t)$, (1)
where g\inC(R, R) and f\in P\equiv{f\in C(R,R);f is w-periodic for some w>0}. The function g is said to be resonant if there exists f\in P such that eq. (1) has no bounded solutions on [0, oo). Using a generalized version' of the Poincare-Birkhoff fixed point theorem, the authors establish conditions on g which guarantee the following result holds: for any f\in P with period w, there exists k\geq 0 such that eq. (1) has infinitely many kw-periodic solutions for every integer k\geq [\bar k]. In such a case, g is clearly non-resonant. |
Keywords： |
|
Classification： |
|
|
|
Download PDF Full-Text
|
|
|
|
