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

共 14 条

[1] Roots of unity and unbounded motions of an asymmetric oscillator [J].

Alonso, JM ;

Ortega, R .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 143 (01) :201-220

[2]

BONHEURE D, SEMINAIRE MATH U CAT, V319

[3] Oscillations of a forced asymmetric oscillator at resonance [J].

Fabry, C ;

Mawhin, J .

NONLINEARITY, 2000, 13 (03) :493-505

[4]

Fonda A, 2006, ADV DIFFERENTIAL EQU, V11, P1111

[5]

Lazer A., 1969, Ann. Mat. Pura Appl, V82, P49, DOI [10.1007/BF02410787, DOI 10.1007/BF02410787]

[6] QUASI-PERIODIC MOTIONS IN SUPERQUADRATIC TIME-PERIODIC POTENTIALS [J].

LEVI, M .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1991, 143 (01) :43-83

[7] Boundedness in nonlinear oscillations at resonance [J].

Liu, B .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 153 (01) :142-174

[8] Boundedness in asymmetric oscillations [J].

Liu, B .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 231 (02) :355-373

[9] Boundedness of solutions for equations with p-Laplacian and an asymmetric nonlinear term [J].

Liu, B .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 207 (01) :73-92

[10]

MOSER J, 1986, SIAM REV, V28, P459, DOI 10.1137/1028153

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