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.

引用

页码：1007 / 1034

页数：28

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