A note on existence of (anti-)periodic and heteroclinic solutions for a class of second-order odes

Nonlinear Analysis, Theory, Methods and Applications

Volumn 70, Issue 4, 2009, Pages 1711-1724

  Wang, Kaizhi ^a   Li, Yong ^a  

^a JILIN UNIVERSITY   (China)

Author keywords

Anti periodic solutions; Heteroclinic solutions; Leray Schauder degree; Variational methods

Indexed keywords

BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; INITIAL VALUE PROBLEMS;

ANTI-PERIODIC; ANTI-PERIODIC SOLUTIONS; FIXED POINTS; HETEROCLINIC SOLUTIONS; LERAY-SCHAUDER DEGREE; VARIATIONAL METHODS;

GREEN'S FUNCTION;

EID: 57049170289     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2008.02.054     Document Type: Article

References (32)

1. Aftabizadeh A., Huang Y., and Pavel N. Nonlinear third-order differential equations with anti-periodic boundary conditions and some optimal control problems. J. Math. Anal. Appl. 192 1 (1995) 266-293
2. Aftabizadeh A., Pavel N., and Huang Y. Anti-periodic oscillations of some second-order differential equations and optimal control problems, Oscillations in nonlinear systems: Applications and numerical aspects. J. Comput. Appl. Math. 52 1-3 (1994) 3-21
3. Aizicovici S., McKibben M., and Reich S. Anti-periodic solutions to nonmonotone evolution equations with discontinuous nonlinearities. Nonlinear Anal. TMA 43 2 (2001) 233-251
4. Aizicovici S., and Reich S. Anti-periodic solutions to a class of non-monotone evolution equations. Discrete Contin. Dynam. Systems 5 1 (1999) 35-42
5. Aizicovici S., and Pavel N. Anti-periodic solutions to a class of nonlinear differential equations in Hilbert space. J. Funct. Anal. 99 2 (1991) 387-408
6. Altman M. A fixed point theorem in Banach space. Bull. Polish Acad. Sci. 5 (1957) 19-22
7. Bangert V. On minimal laminations of a torus. AIHP Anal. Nonlin. 6 (1989) 95-138
8. Bonheure D., and Fabry C. Periodic motions in impact oscillators with perfectly elastic bounces. Nonlinearity 15 (2002) 1281-1297
9. Budd J. The global dynamics of impact oscillators. Real and Complex Dynamical Systems. Nato Adv. Sci. Inst. Series C, Math. Phys. Sci. vol. 644 (1995), Kluwer, Dordrecht 27-46
10. Budd J., and Dux F. Intermittency in impact oscillators close to resonance. Nonlinearity 7 (1994) 1191-1224
11. Chen Y. Anti-periodic solutions for semilinear evolution equations. J. Math. Anal. Appl. 315 1 (2006) 337-348
12. Chen Y., Kim J., and Li Y. Viscosity periodic and anti-periodic solutions for nonlinear equations. Nonlinear Funct. Anal. Appl. 10 2 (2005) 173-177
13. +). Math. Nachr. 278 4 (2005) 356-362
14. Chen Y. On Massera's theorem for anti-periodic solution. Adv. Math. Sci. Appl. 9 1 (1999) 125-128 (English summary)
15. Denzler J. Mather sets for plane Hamiltonian systems. ZAMP. 38 (1987) 791-812
16. Ekeland I. Convexity Methods in Hamiltonian Mechanics (1990), Springer, Berlin, NewYork
17. Franco D., and Nieto J. First-order impulsive ordinary differential equations with anti-periodic and nonlinear boundary conditions. Nonlinear Anal. TMA 42 2 (2000) 163-173
18. Jiang M. Periodic solutions of second order differential equations with discontinuous nonlinearities. J. Dynam. Differential Equations 18 4 (2006) 1043-1067
19. Moser J. Minimal solutions of variational problems on a torus. AIHP Anal. Nonlin. 3 (1986) 229-272
20. Nakao M. Existence of an anti-periodic solution for the quasilinear wave equation with viscosity. J. Math. Anal. Appl. 204 3 (1996) 754-764
21. Okochi H. On the existence of anti-periodic solutions to nonlinear parabolic equations in noncylindrical domains. Nonlinear Anal. 14 9 (1990) 771-783
22. Picard E. Sur l'application des méthodes d'approximations successives à l'étude de certaines équations différentielles ordinaires. J. Math. 9 (1893) 217-271
23. Qian D., and Sun X. Invariant tori of asymptotically linear impact oscillators. Sci. China A 49 5 (2006) 669-687
24. Qian D., and Torres P. Periodic motions of linear impact oscillators via the successor map. SIAM J. Math. Anal. 36 (2005) 1707-1725
25. Qian D., and Torres P. Bouncing solutions of an equation with attractive singularity. Proc. R. Soc. Edinb. A 134 (2004) 201-213
26. Rabinowitz P., and Stredulinsky E. On some results of Moser and of Bangert. AIHP Anal. Nonlin. 21 (2004) 673-688
27. Rabinowitz P., and Stredulinsky E. Mixed states for an Allen-Cahn type equation. Comm. Pure Appl. Math. 56 (2003) 1078-1134
28. Rabinowitz P. Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS. Regional Conference Series in Mathematics vol. 65 (1986), American Mathematical Society, Providence, RI
29. Souplet P. Optimal uniqueness condition for the antiperiodic solutions of some nonlinear parabolic equations. Nonlinear Anal. 32 2 (1998) 279-286
30. Yin Y. Monotone iterative technique and quasilinearization for some anti-periodic problems. Nonlinear World 3 2 (1996) 253-266
31. Yin Y. Anti-periodic solutions of some semilinear parabolic boundary value problems. Dynam. Contin. Discrete Impuls. Systems 1 2 (1995) 283-297
32. Yin Y. Remarks on first order differential equations with anti-periodic boundary conditions. Nonlinear Times Digest 2 1 (1995) 83-94