| 一类二阶四点边值问题正解的存在性 |
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| 引用本文： | 魏玉冬,陈爱江,白随平.一类二阶四点边值问题正解的存在性[J].数学的实践与认识,2007,37(4):139-144. |
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| 作者姓名： | 魏玉冬 陈爱江 白随平 |
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| 作者单位： | 1. 河北经贸大学数学与统计学学院,河北,石家庄,050061
2. 保定金融高等专科学校,河北,保定,071009 |
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| 摘 要： | 讨论二阶四点微分方程组边值问题u″+p(t)f(t,u(t),v(t))=0,0 t 1,v″+q(t)g(t,u(t),v(t))=0,0 t 1,u(0)=a1x(ξ1),u(1)=b1x(η1)v(0)=a2x(ξ2),v(1)=b2x(η2)如果函数f,g:0,1]×0,∞)×0,∞)→0,∞)是连续的,并赋予f、g一定的增长条件,利用Leggett-Williama不动点定理,证明了上述边值问题至少存在三对正解.
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| 关 键 词： | 正解 Leggett-Williama不动点定理 锥 凹泛函 |
| 修稿时间： | 2006年11月15 |
The Existence of Positive Solutions of Boundary Value Problems for a Class of Second-order Differential Equation System |
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| WEI Yu-dong,CHEN Ai-jiang,BAI Sui-ping.The Existence of Positive Solutions of Boundary Value Problems for a Class of Second-order Differential Equation System[J].Mathematics in Practice and Theory,2007,37(4):139-144. |
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| Authors: | WEI Yu-dong CHEN Ai-jiang BAI Sui-ping |
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| Abstract: | We apply Leggett-Williams fixed point theorem to discuss multi-point boundary value problem of the second-order differential equation system u″+p(t)f(t,u(t),v(t))=0,0t1, v″+q(t)g(t,u(t),v(t))=0, 0t1, u(0)=a1x(ξ1), u(1)=b1x(η1) v(0)=a2x(ξ2), v(1)=b2x(η2)where f,g:×0,∞)×0,∞)→0,∞) are continuous,growth conditions are imposed on f,g,which yield the existence of at least three positive solutions for the system. |
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| Keywords: | positive solution fixed points theorem cone |
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