A relationship between the periodic and the Dirichlet BVPs of singular differential equations

Royal Society of Edinburgh - Proceedings A

Volumn 128, Issue 5, 1998, Pages 1099-1114

  Zhang, Meirong ^a,b  

^a TSINGHUA UNIVERSITY   (China)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041392487     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500030080     Document Type: Article

References (27)

1. A. Ambrosetti. Critical points and nonlinear variational problems. Mem. Soc. Math. France 49, in Bull. Soc. Math. France 120 (1992), 5-132.
2. A. Ambrosetti and V. Coti Zelati. Critical points with lack of compactness and singular dynamical systems. Ann. Mat. Pura Appl. (4) 149 (1987), 237-59.
3. A. Bahri and P. Rabinowitz. A minimax method for a class of Hamiltonian systems with singular potentials. J. Funct. Anal. 82 (1989), 412-28.
4. V. Bevc, J. L. Palmer and C. Süsskind. On the design of the transition region of axi-symmetric magnetically focused beam valves. J. British Inst. Radio Engineers 18 (1958), 696-708.
5. A. Capietto, J. Mawhin and F. Zanolin. Continuation theorems for periodic perturbations of autonomous systems. Trans. Amer. Math. Soc. 329 (1992), 41-72.
6. V. Coti Zelati. Dynamical systems with effective-like potentials. Nonlinear Anal. 12 (1988), 209-22.
7. M. A. del Pino and R. F. Manásevich. Infinitely many T-periodic solutions for a problem arising in nonlinear elasticity. J. Differential Equations 103 (1993), 260-77.
8. M. A. del Pino, R. F. Manásevich and A. Montera. T-periodic solutions for some second-order differential equations with singularities. Proc. Roy. Soc. Edinburgh Sect. A 120 (1992), 231-43.
9. T. Ding. A boundary value problem for the periodic Brillouin focusing system. Acta Sci. Natur. Univ. Pekinensis 11 (1965), 31-8 [in Chinese].
10. T. Ding, R. Iannacci and F. Zanolin. Existence and multiplicity results for periodic solutions of semilinear Duffing equations. J. Differential Equations 105 (1993), 364-409.
11. A. Fonda, R. Manásevich and F. Zanolin. Subharmonic solutions for some second order differential equations with singularities. SIAM J. Math. Anal. 24 (1993), 1294-311.
12. W. Gordon. Conservative dynamical systems involving strong forces. Trans. Amer. Math. Soc. 204 (1975), 113-35.
13. P. Habets and L. Sanchez. Periodic solutions of some Liénard equations with singularities. Proc. Amer. Math. Soc. 109 (1990), 1035-44.
14. P. Habets and L. Sanchez. Periodic solutions of dissipative dynamical systems with singular potentials. Differential Integral Equations 3 (1990), 1139-49.
15. A. C. Lazer and S. Solimini. On periodic solutions of nonlinear differential equations with singularities. Proc. Amer. Math. Soc. 99 (1987), 109-14.
16. P. Majer. Ljusternik-Schnirelmann theory with local Palais-Smale conditions and singular dynamical systems. Ann. Inst. H. Poincaré Anal. Non Linéaire 8 (1991), 459-76.
17. P. Majer and S. Terracini. Periodic solutions to some problems of n-body type. Arch. Rational Mech. Anal. 124 (1993), 381-404.
18. J. Mawhin. Topological Degree Methods in Nonlinear Boundary Value Problems, CBMS - Regional Conference Series in Mathematics 40 (Providence, RI: American Mathematical Society, 1979).
19. J. Mawhin. Topological degree and boundary value problems for nonlinear differential equations. In Topological Methods for Ordinary Differential Equations, eds M. Furi and P. Zecca, pp. 74-142, Lecture Notes in Mathematics 1537 (New York/Berlin: Springer, 1993).
20. J. Mawhin and J. R. Ward. Nonuniform non-resonance conditions at the two first eigenvalues for periodic solutions of forced Liénard and Duffing equations. Rocky Mountain J. Math. 12 (1982), 643-54.
21. S. Solimini. On forced dynamical systems with a singularity of repulsive type. Nonlinear Anal. 14 (1990), 489-500.
22. G. Talenti. Best constant in Sobolev inequality. Ann. Mat. Pura Appl. (4) 110 (1976), 353-72.
23. C. Wang. Multiplicity of periodic solutions for Duffing equations under nonuniform non-resonance conditions (Preprint).
24. Y. Ye and X. Wang. Nonlinear differential equations in electron beam focusing theory. Acta Math. Appl. Sinica 1 (1978), 13-41 [in Chinese].
25. M. Zhang. Periodic solutions of Liénard equations with singular forces of repulsive type. J. Math. Anal. Appl. 203 (1996), 254-69.
26. M. Zhang. Periodic solutions of damped differential systems with repulsive singular forces (Preprint).
27. S. Zhang. Multiple closed orbits of fixed energy for N-body-type problems with gravitational potentials. J. Math. Anal. Appl. 208 (1997), 462-75.