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| BOUNDEDNESS OF SOLUTIONS FOR SUPERLINEAR REVERSIBLE SYSTEMS |
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Citation： |
LI Xiong.BOUNDEDNESS OF SOLUTIONS FOR SUPERLINEAR REVERSIBLE SYSTEMS[J].Chinese Annals of Mathematics B,2001,22(1):31~46 |
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Net amount： 1016 |
Authors： |
LI Xiong; |
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| Abstract： |
This paper is concerned with the boundedness of solutions for second order differential equations $\ddot{x} + f(x, t) \dot{x} + g(x,t) = 0$, which are neither dissipative nor conservative, and where the functions f and g are odd in x and even in t, which are 1-periodic in t, and the function g satisfies $\frac{g(x, t)}{x} \rightarrow +\infty$, as $\|x\| \rightarrow +\infty$. Using the KAM theory for reversible systems, the author proves the existence of invariant tori and thus the boundedness of all the solution and the existence of quasiperiodic solutions and subharmonic solutions. |
Keywords： |
Boundedness of solutions, Quasiperiodic solutions, Subharmonic solutions, KAM theory, Reversible systems |
Classification： |
34C15, 58F27 |
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