| 一类四阶两点常微分边值问题解的存在唯一性 |
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| 引用本文： | 席进华. 一类四阶两点常微分边值问题解的存在唯一性[J]. 甘肃联合大学学报(自然科学版), 2001, 15(1): 4-7 |
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| 作者姓名： | 席进华 |
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| 作者单位： | 合作民族师范高等专科学校 数学系, |
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| 摘 要： | 对于四阶两点常微分方程边值问题y( 4) =f ( x,y) ,y( a) =y( b) =y"( a) =y"( b) =0 ,其中 f ( x,y) :[a,b]× R→R连续 ,且满足 L ipschits条件 ,给出在 Banach压缩映象原理下的解的存在唯一性 ,并通过对 C[a,b]的范数的改造 ,给出最优结果 .
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| 关 键 词： | 边值问题 四阶常微分方程 解的存在唯一性 解 |
| 文章编号： | 1007-9912(2001)01-0004-04 |
| 修稿时间： | 2000-06-01 |
Existence and Uniqueness Theorems for Fourth-Order Boundary Value Problems |
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| XI Jin-hua. Existence and Uniqueness Theorems for Fourth-Order Boundary Value Problems[J]. Journal of Gansu Lianhe University :Natural Sciences, 2001, 15(1): 4-7 |
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| Authors: | XI Jin-hua |
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| Abstract: | This paper intends to prove that the two-point boundary value problem,namely y(4)=f(x,y),y(a)=y(b)=y＂(a)=y＂(b)=0,has a unique solution provided (17)/(384)k(b-a)4＜1 with the lipschits condition and to prove that the two-point boundary value problem has a unique solution provided ((b-a)4)/(π4)k＜1 with the norm of the space C［a,b］. |
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| Keywords: | bourdary value problem fourth-order difference equation existence and uniqueness solution |
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