| 张祖峰,魏章志.共振条件下四阶四点边值问题的可解性[J].数学研究及应用,2008,28(4):935~944 |
| 共振条件下四阶四点边值问题的可解性 |
| Solvability of 4-Point Boundary Value Problems at Resonance for Fourth-Order Ordinary Differential Equations |
| 投稿时间：2006-09-23 修订日期：2007-01-19 |
| DOI：10.3770/j.issn:1000-341X.2008.04.025 |
| 中文关键词: 四阶方程 共振 重合度. |
| 英文关键词:fourth order equation resonance coincidence degree. |
| 基金项目:宿州学院硕士科研启动基金(No.2008yss19). |
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| 中文摘要: |
| 本文讨论四阶常微分方程$$x^{(4)}(t)=f(t,x(t),x'(t),x''(t),x'''(t)),\;\;\;t\in(0,1), \eqno (E)$$在边值条件$$x(0)=x(1)=0,\;\alpha x''(\xi_1)-\beta x'''(\xi_1)=0,\;\gamma x''(\xi_2)+\delta x'''(\xi_2)=0, \eqno(B)$$满足共振情形: $\alpha \delta+\beta\gamma+\alpha\gamma(\xi_2-\xi_1) |
| 英文摘要: |
| In this paper, we consider the following fourth order ordinary differential equation $$x^{(4)}(t)=f(t,x(t),x'(t),x''(t),x'''(t)),~~t\in(0,1) \tag E$$ with the four-point boundary value conditions: $$x(0)=x(1)=0,\; \alpha x''(\xi_1)-\beta x'''(\xi_1)=0,\;\gamma x''(\xi_2)+\delta x'''(\xi_2)=0, \tag B$$ where $0<\xi_1<\xi_2< 1.$ At the resonance condition $\alpha \delta+\beta\gamma+\alpha\gamma(\xi_2-\xi_1)=0,$ an existence result is given by using the coincidence degree theory. We also give an example to demonstrate the result. |
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