PDF(533 KB)
PDF(533 KB)
PDF(533 KB)
扭转性质和无先验界的二阶微分方程
Twist Property and the Second Order Differential Equations Without a Priori Bounds
周期解的存在性 / 二阶微分方程 / 扭转不动点定理 {{custom_keyword}} /
existence of periodic solutions / second order differential equations / twist fixed point theorem {{custom_keyword}} /
[1] Mawhin J., Wilem M., Critical Point Theory and Hamiltonian Systems, New York: Springer-Verlag, 1989.
[2] Jiang M., Periodic solutions of second order differential equations with an obstacle, Nonlinearity, 2006, 19: 1165--1183.
[3] Qian D., Infinity of subharmonics for asymmetric Duffing equations with Lazer-Leach-Dancer condition, J. Differential Equations, 2001, 171: 233--250.
[4] Ding T., Zanolin F., Time-maps for thesolvability of periodically perturbed nonlinear Duffing equations, Nonlinear Analysis TMA, 1991, 17: 635--653.
[5] Ding T., Zanolin F., Periodic solutions of Duffing's equations with superquadratic potential, J. Differential Equations, 1992, 97: 328--378.
[6] Ding T., Iannacci R., Zanolin F., Existence and multiplicity results for periodic solutions of semilinear Duffing equations, J. Differential Equations, 1993, 105: 364--409.
[7] Ding W. Y., The fixed point of twist map and the periodic solutions of ordinary differential equations, Acta Mathematica Sinica, Chinese Series, 1982, 25(2): 227--235.
[8] Hartman P., On boundary value problems for superlinear second order differential equations, J. Differential Equations, 1977, 26: 37--53.
[9] Jacobowitz H., Periodic solutions of x''+f(t,x)=0 via the Poincar\'e-Birkhoff theorem, J. Differential Equations, 1976, 20: 37--52. indent=6mm
[10] Capietto A., Mawhin J., Zanolin F., Continuation theorems for periodic perturbations of autonomous systems, Trans. Amer. Math. Soc., 1992, 329: 41--72.
[11] Capietto A., Mawhin J., Zanolin F., A Continuation theorem for periodic boundary value problems with oscillatory nonlinearities, Nonlinear Differential Equations and Applications, 1995, 2: 133--163.
[12] Coffmann C., Ulrich D., On the continuation of solutions of a certain nonlinear differential equation, Monatsh. Math., 1967, 71: 385--392.
[13] Moser J., Zehnder E., Notes on Dynamical Systems, Courant Lecture Notes in Mathematics, New York: Courant Institute of Mathematical Sciences, 2005.
[14] Qian D., Periodic solutions for second order equations with time-dependent potential via time map, J. Math. Anal. Appl., 2004, 294: 361--372.
[15] Qian D., On forced nonlinear oscillations for the second order equations with semiquadratic potential, Nonlinear Analysis TMA, 1996, 26: 1715--1731.
国家自然科学基金(10571131); 教育部博士点基金(20070285002);江苏省自然科学基金(BK2006046)
/
| 〈 |
|
〉 |
