Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Second order singular periodic problems in the presence of dry friction


Authors: A. Cabada and L. Sanchez
Journal: Proc. Amer. Math. Soc. 131 (2003), 2137-2144
MSC (2000): Primary 34B15, 34C25
Published electronically: October 24, 2002
MathSciNet review: 1963760
Full-text PDF Free Access

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 [Enhancements On Off] (What's this?)

  • 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: http://dx.doi.org/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
Published electronically: 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
Article copyright: © Copyright 2002 American Mathematical Society