一类周期边值共振问题的可解性On the Solvability of Some NonlinearPeriodic Boundary Value Problems at Resonance
马如云
摘要(Abstract)：
本文研究带周期非线性项的二阶常微分方程周期边值共振问题的可解性,该方程对应的泛函不满足[P.S.]条件,该文是通过建立不同维数的link所产生的不同类集族之间的联系来证明临界点的存在性的。
关键词(KeyWords)： Duffing方程;周期边值问题;共振
基金项目(Foundation):
作者(Author): 马如云
参考文献(References)：
- 1 Sorimini S. On the solvability of some elliptic partial differential equations with the linear part at resonance. J Math Analy & Appli, 1986; 117(1) : 138～152
- 2 lannacci R, Nkashama M N. Unbounded perturbations of forced second ordinary differential equations at resonance. J Differential Equation, 1987; 69: 289～309
- 3 Mawhin J, Willem M. Multiple solutions of the periodic BVP for some forced Pendulum-type equation. J Defferential Equation, 1984; 52: 264～286
- 4 Ward J R. A boundayr value problem with a periodic nonlinearity. Nonlinear Analysis, 1986; 10(2) : 207～213
- 5 Massabo I, Pesachowicz J On the connectivity properties of the solution set of parametrized families of compact vectoy fields. JFunctional Analysis, 1984; 59(2) : 151～166
- 6 Bartoio P, Bencj V, Fortunato D. Abstract critical point theorems and applications to some nonlinear problems with "strong" resonance at infinity. Nonlinear Analysis, 1983; 7(9) : 981～1012
- 7 Tersian S A. A minimax theorem and applications to nontesonance problems for semilinear equations. Nonlinear Analysis, 1986; 10(7) : 651～668
- 8 张恭庆.临界点理论及其应用.上海科技版,1986