| 一类二阶泛函微分方程解的平方可积性和有界性 |
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| 引用本文： | 孟东沅.一类二阶泛函微分方程解的平方可积性和有界性[J].数学的实践与认识,2006,36(5):251-257. |
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| 作者姓名： | 孟东沅 |
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| 作者单位： | 青岛理工大学理学院,山东,青岛,266555 |
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| 摘 要： | 讨论了二阶泛函微分方程x(″t)+p(t)x(′t)+q1(t)x(t)+q2(t)x(t-τ)=f(t)通过构造一类泛函,借助于两个重要不等式建立了其属于L.S或L.S∩L.C(L.S表示解有界,L.C表示平方可积)的充分条件.
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| 关 键 词： | 微分方程 平方可积性 有界性 |
| 修稿时间： | 2005年6月27日 |
Quadrtic Integability and Boundedness of Solutionsof a Class of Functional Differential Equations |
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| MENG Dong-yuan.Quadrtic Integability and Boundedness of Solutionsof a Class of Functional Differential Equations[J].Mathematics in Practice and Theory,2006,36(5):251-257. |
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| Authors: | MENG Dong-yuan |
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| Abstract: | In this paper,with the aid of auxiliary founctions ah inequalities,we consider the second order nonhomogeneous functional differential equationx″(t)+p(t)x′(t)+q_1(t)x(t)+q_2(t)x(t-τ)=f(t)where we assume that equation(1) exists solution.We obtain some sufficient cnditions under which all solutions x(t) of equation(1) belong to L.S or L~22,∞)∩L~∞2,∞). |
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| Keywords: | differential equation quadratic integrability boundedness |
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