Periodic solutions of second order differential equations with discontinuous nonlinearities

Journal of Dynamics and Differential Equations

Volumn 18, Issue 4, 2006, Pages 1043-1067

  Jiang, Mei Yue ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

Discontinuous nonlinearities; Periodic solutions

Indexed keywords

EID: 33750016004     PISSN: 10407294     EISSN: 15729222     Source Type: Journal    
DOI: 10.1007/s10884-006-9028-z     Document Type: Article

References (25)

1. Amann, H., and Zehnder, E. (1980). Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations, Ann. Scuola Normale Superiors di Pisa 7, 539-603.
2. Chang, K.-C. (1980). The obstacle problem and partial differential equations with discontinuous nonlinearities. Comm. Pure Appl. Math. 33, 117-146.
3. Chang, K.-C. (1981). Variational methods for non-differentiable functional and their applications to partial differential equations. J. Math. Anal. Appl. 80, 102-129.
4. Chang, K.-C. (1981). Solutions of asymptotically linear operator equations via Morse theory. Comm. Purs Appl. Math. 34, 693-712.
5. Chang, K.-C. (1986). Applications of homology theory to some problems in differential equations. In Browder, F.E. (Ed.), Proceedings Symposium on Pure Mathematics, Vol. 45, AMS, Providence, pp. 253-262.
6. Conley, C., and Zehnder, E. (1983). The Birkhoff-Lewis fixed point theorem and a conjecture of Arnold. V.-I., Invent. Math. 73, 33-49.
7. Ding, T., and Zanolin, F. (1992). Periodic solutions of Duffing's equation with superquadratic potential, J. Diff. Eq. 97, 328-378.
8. Ding, W. (1982). Fixed points of twist mappings and periodic solutions of ordinary differential equations. Acta Math. Sinica. 25, 227-235 (In Chinese).
9. Ekeland, I. (1990). Convexity Methods in Hamiltonian Dynamics. Springer-Verlag, Berlin.
10. Ghoussoub, N. (1993). Duality and Perturbation Methods in Critical Point Theory, Cambridge University Press, Cambridge.
11. Jacobowitz, H. (1977). Periodic solutions of ẍ + f(t, x) = 0 via the Poincaré-Birkhoff theorem, J. Diff. Eq. 20, 37-52;
12. Corrigendum 25, 148-149.
13. Jiang, M.-Y. (1999). On a theorem by Mather and Aubry-Mather sets for planar Hamiltonian systems. Sci. China, 44, 1121-1128.
14. Jiang, M.-Y. (2004). Solutions of a resonant elliptic equation. Research Report No. 92. Institute of Mathmatics, Peking University.
15. Jiang, M.-Y. (2006). Periodic solutions of second order differential equations with an obstacle. Nonlinearity 19, 1165-1183.
16. Jiang, M.-Y. and Pei, M.-L. (1993). Aubry-Mather sets for planar superlinear Hamiltonian systems. Dyn. Syst. Appl. 2, 189-200.
17. Lazer, A. C. and McKenna, P. J. (1992). Periodic bouncing for a forced linear spring with obstacle, Diff. Integr. Eqs. 5, 165-172.
18. Liu, J.-Q. (1989). A generalized saddle popint theorem, J. Diff. Eqs. 82, 372-385.
19. Ortega, R. (2002). Dynamics of a forced oscillator with obstacle. In Variational and Topological Methods in the Study of Nonlinear Phenomena. Birkhauser, Boston-Basel-Berlin, pp. 75-87.
20. Rabinowitz, P. H. (1986). Minimax methods in critical point theory with applications to differential equations. In CBMS, Regional Conf. Ser. in Math., 65. American Mathematics Society, Providence, RI.
21. Ramos, M., Terracini, S., and Troesler, C. (1998). Superlinear indefinite elliptic problems and Pohozaev type identities. J. Funct. Anal. 159, 596-628.
22. Qian, D. B., and Torres, P. (2004). Periodic periodic solutions of equation with attractive singularity. Proc. Roy. Soc. Edingburgh 134A, 201-213.
23. Qian, D. B., and Torres, P. (2005). Periodic motions of linear impact oscillators via the successor map. SIAM J. Math. Anal. 36, 1707-1725.
24. Wang, Z.-Q. (2001). Nonlinear boundary value problems with concave nonlinearities near the origin, NoDEA, 8, 15-33.
25. Willem, M. (1996). Minimax Theorems. Birkhäuser, Boston-Basel-Berlin.