| 二阶多点边值问题多个正解存在性 |
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| 引用本文： | 魏玉冬,白随平,姚立.二阶多点边值问题多个正解存在性[J].数学的实践与认识,2007,37(5). |
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| 作者姓名： | 魏玉冬 白随平 姚立 |
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| 作者单位： | 河北经贸大学,数学与统计学学院,河北,石家庄,050061 |
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| 摘 要： | 利用Leggett-Williams不动点定理,并赋予f,g一定的增长条件,证明了二阶多点微分方程组边值问题u″+f(t,u,v)=0,v″+g(t,u,v)=0,0≤t≤1,u(0)=v(0)=0,u(1)-∑n-2i=1kiu(ξi)=0,v(1)-∑m-2i=1liv(ηi)=0,至少存在三对正解,其中f,g:0,1]×0,∞)×0,∞)→0,∞)是连续的.
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| 关 键 词： | Leggett-Williams不动点定理 锥 正解 |
The Existence of Multiple Positive Solutions for Second-order Multiple Points Boundary Value Problem Systems |
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| WEI Yu-dong,BAI Sui-ping,YAO Li.The Existence of Multiple Positive Solutions for Second-order Multiple Points Boundary Value Problem Systems[J].Mathematics in Practice and Theory,2007,37(5). |
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| Authors: | WEI Yu-dong BAI Sui-ping YAO Li |
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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″+f(t,u,v)=0,0≤t≤1,v″+g(t,u,v)=0,0t1,u(0)=0,u(1)-∑n-2i=1kiu(ξi)=0,v(0)=0,v(1)-∑m-2i=1liv(ηi)=0,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: | Leggett-Williams fixed point theorem cone positive solution |
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