|
Second order singular periodic problems in the presence of dry friction
Author(s):
A.
Cabada;
L.
Sanchez
Journal:
Proc. Amer. Math. Soc.
131
(2003),
2137-2144.
MSC (2000):
Primary 34B15, 34C25
Posted:
October 24, 2002
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We prove, via an approach by ordinary differential equations, the existence of oscillations for second order inclusions with restoring terms with singularities both of repulsive and attractive type and with a dry friction term.
References:
-
- 1.
- Bonheure D. and De Coster C., Forced singular oscillators and the method of lower and upper solutions, Séminaire de Mathématique, Univ. Catholique de Louvain, Rapport n. 320, Jan. 2002.
- 2.
- Bothe D., Periodic solutions of non-smooth friction oscillators, Z. Angew. Math. Phys. 50 (1999), 779-808. MR 2000f:34078
- 3.
- Deimling K., Nonlinear Functional Analysis, Springer 1985. MR 86j:47001
- 4.
- Deimling K., Resonance and Coulomb friction, Differential and Integral Equations 7 (1994), 759-765. MR 95b:34030
- 5.
- Deimling K. and Szilágyi P., Periodic solutions of dry friction problems, Z. Angew. Math. Phys. 45, (1994), 53-60. MR 94m:34099
- 6.
- Filippov A. F., Differential Equations with Discontinuous Righthand Sides, Kluwer Acad. Publ., Dordrecht 1988. MR 90i:34002
- 7.
- Guenther R. B., Lee J. W. and Senkyrik, M., The Filippov approach to boundary and initial value problems and applications, Henderson, Johnny (ed.), Boundary value problems for functional differential equations, Singapore: World Scientific, 153-163 (1995). MR 96m:34034
- 8.
- Habets P. and Sanchez L., Periodic solutions of some Liénard equations with singularities, Proc. Amer. Math. Soc. 109 (1990), 1035-1044. MR 90k:34049
- 9.
- Kunze M., Non-smooth dynamical systems, Lecture Notes in Mathematics 1744, Springer 2000. MR 2002e:34002
- 10.
- Lazer A. C. and Solimini S., On periodic solutions of nonlinear differential equations with singularities, Proc. Amer. Math. Soc. 99 (1987), 109-114. MR 87k:34064
- 11.
- Mawhin J., Some remarks on semilinear problems at resonance where the nonlinearity depends only on the derivatives, Acta Math. et Informatica Univ. Ostraviensis 2 (1994), 61-69. MR 95j:34031
- 12.
- Senkyrik, M., Periodic solutions of a second order differential equation with discontinuities in the spatial variable, Top. Methods in Nonlinear Analysis (1995), 199-206. MR 97d:34041
- 13.
- Senkyrik, M. and Guenther, R. B., Boundary value problems with discontinuities in the spatial variable, J. Math. Anal. Applications 193 (1995), 296-305. MR 96c:34038
- 14.
- Torres, P. J., Periodic solutions of some differential equations with nonlinear damping, Differential Integral Equations 15 (2002), 17-32.
- 15.
- Zhang M., Periodic solutions of damped differential systems with repulsive singular forces, Proc. Amer. Math. Soc. 127 (1999), 401-407. MR 99k:34092
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
34B15, 34C25
Retrieve articles in all Journals with MSC
(2000):
34B15, 34C25
Additional Information:
A.
Cabada
Affiliation:
Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
Email:
cabada@usc.es
L.
Sanchez
Affiliation:
Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Avenida Professor Gama Pinto, 2, 1649-003 Lisboa, Portugal
Email:
sanchez@lmc.fc.ul.pt
DOI:
10.1090/S0002-9939-02-06766-7
PII:
S 0002-9939(02)06766-7
Received by editor(s):
October 23, 2001
Received by editor(s) in revised form:
February 18, 2002
Posted:
October 24, 2002
Additional Notes:
The first author's research was supported by D.G.I. project BFM 2001--3884--C02--01 and Acción integrada Hispano - Lusa HP199-0026
The second author's research was supported by Fundação para a Ciência e a Tecnologia and Acção Integrada Luso-Espanhola E/93-00
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2002,
American Mathematical Society
|
Comments: webmaster@ams.org