Twist solutions of a Hill's equation with singular term

Advanced Nonlinear Studies

Volumn 2, Issue 3, 2002, Pages 279-287

  Torres, Pedro J ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

Brillouin equation; Lyapunov stability; Twist solution; Upper and lower solutions

Indexed keywords

EID: 0037629759     PISSN: 15361365     EISSN: None     Source Type: Journal    
DOI: 10.1515/ans-2002-0305     Document Type: Article

References (16)

1. a, Diff. Eqns. 8 (1972), 1609-1612.
2. V. Bevc, J.L. Palmer and C. Süsskind, On the design of the transition region of axisymmetric magnetically focusing beam valves, J. British Inst. Radio Engineers 18 (1958), 696-708.
3. C. De Coster and P. Habets, Upper and lower solutions in the theory of ODE boundary value problems: classical and recent results, in Nonlinear Analysis and Boundary Value Problems for Ordinary Differential Equations, ed. F. Zanolin, CISM-ICMS courses and lectures 371, Springer-Verlag, New York, 1996.
4. T. Ding, A boundary value problem for the periodic Brullouin focusing system, Acta Sci. Natur. Univ. Pekinensis, 11 (1965), 31-38. [In Chinese]
5. W. Magnus and S. Winkler, Hill's equation, Dover, New York, 1966.
6. L. Markus and K.R. Meyer, Periodic orbits and solenoids in generic hamuiltonian dynamical systems, Am. J. Math. 102 (1980), 25-92.
7. R. Moeckel, Generic bifurcations of the twist coefficient, Ergodic Theory Dynam. Systems 10 (1990), 185-195.
8. R. Ortega, The twist coefficient of periodic solutions of a time-dependent Newton's equation, J. Dynam. Differential Equations 4 (1992), 651-665.
9. R. Ortega, Periodic solutions of a newtonian equation: stability by the third approximation, J. Diff. Eqns. 128 (1996), 491-518. (Pubitemid 126162931)
10. R. Ortega, The number of stable periodic solutions of time-dependent Hamiltonian systems with one degree of freedom, Ergodic Theory Dynam. Systems 18 (1998), 1007-1018.
11. -3 = 0, Proc. Am. Math. Soc. 1 (1950), 681.
12. C. Siegel and J. Moser, Lectures on Celestial Mechanics, Springer-Verlag, Berlin, 1971.
13. P. J. Torres, Existence and uniqueness of elliptic periodic solutions of the Brillouin electron beam focusing system, Math. Met. Appl. Sci. 23 (2000), 1139-1143.
14. Y. Ye and X. Wang, Nonlinear differential equations in electron beam focusing theory, Acta Math. Appl. Sinica 1 (1978), 13-41. [In Chinese]
15. M. Zhang, Periodic solutions of Liénard equations with singular forces of repulsive type, J. Math. Anal. Appl. 203 (1996), 254-269. (Pubitemid 126170748)
16. M. Zhang, A relationship between the periodic and the Dirichlet BVPs of singular differential equations, Proc. Roy. Soc. Edinbourgh Sect. A 128 (1998), 1099-1114.