On the boundedness of solutions to a nonlinear singular oscillator

被引：18
|
作者：
Capietto, Anna [2 ]
Dambrosio, Walter [2 ]
Liu, Bin [1 ]
机构：
[1] Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China
[2] Univ Turin, Dipartimento Matemat, I-10123 Turin, Italy
来源：
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2009年 / 60卷 / 06期
关键词：
Singular potential; boundedness; Moser's twist theorem; Aubry-Mather sets; ASYMMETRIC OSCILLATOR; EQUATIONS; RESONANCE; MOTIONS;
D O I：
10.1007/s00033-008-8094-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study a second order scalar equation of the form x'' + V'(x) = p(t), where p is a pi-perodic function and V is a singular potential. We give sufficient conditions on V, p ensuring that all solutions are bounded; we prove the existence of Aubry-Mather sets as well.
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页码：1007 / 1034
页数：28
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