| 非线性2n阶微分方程的非线性两点边值问题解的存在性 |
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| 引用本文： | 高永馨,谢燕华.非线性2n阶微分方程的非线性两点边值问题解的存在性[J].黑龙江大学自然科学学报,2009,26(5). |
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| 作者姓名： | 高永馨 谢燕华 |
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| 作者单位： | 中国民航大学理学院,天津,300300 |
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| 摘 要： | 利用上下解的方法研究了非线性2n阶常微分方程y(2n)=f(t,y,y′,…,y(2n-1))满足如下边界条件条件g0(y(a),y′(a))=0,g1(y′(a),y″(a),…,y(2n-3)(a))=0,g2(y(2n-2)(a),y(2n-1)(a))=0,h0(y(c),y′(c),y″(c))=0,hi(y(i)(c),y(i+1)(c))=0(i=3,4,…,2n-2).的非线性两点边值问题解的存在性.
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| 关 键 词： | 非线性2n阶微分方程 非线性两点边值问题 解的存在性 |
Existence of solutions to nonlinear two-point boundary value problems for 2nth-order nonlinear differential equation |
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| GAO Yong-xin,XIE Yan-hua.Existence of solutions to nonlinear two-point boundary value problems for 2nth-order nonlinear differential equation[J].Journal of Natural Science of Heilongjiang University,2009,26(5). |
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| Authors: | GAO Yong-xin XIE Yan-hua |
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| Institution: | College of Science;Civil Aviation University of China;Tianjin 300300;China |
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| Abstract: | By using the method of upper-lower solutions,the sufficient conditions are given for the existence of solutions to nonlinear two point boundary value problems for nonlinear 2nth-order differential equation y~((2n))=f(t,y,y',...,y~((2n-1))) with the boundary conditions g_0(y(a),y'(a)) =0,g_1(y'(a),y"(a),...,y~((2n-3))(a)) =0,g_2(y~((2n-2))(a),y~((2n-1))(a)) =0,h_0(y(c),y'(c),y"(c))=0,h_i(y~((i))(c),y~((i+1))(c))=0(i=3,4,...,2n-2). |
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| Keywords: | nonlinear 2nth-order differential equation nonlinear two point boundary value problems existence of solutions |
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