| 非线性四阶周期边值问题多个正解的存在性 |
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| 引用本文： | 黎定仕,刘文斌,徐丛丛,张伟伟.非线性四阶周期边值问题多个正解的存在性[J].数学的实践与认识,2008,38(16). |
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| 作者姓名： | 黎定仕 刘文斌 徐丛丛 张伟伟 |
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| 作者单位： | 中国矿业大学,理学院,江苏,徐州,221008 |
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| 摘 要： | 利用不动点和度理论,证明了四阶周期边值问题u(4)(t)-βu″(t)+αu(t)=λf(t,u(t)),0≤t≤1,u(i)(0)=u(i)(1),i=0,1,2,3,至少存在两个正解,其中β>-2π2,0<α<(1/2β+2π2)2,α/π4+β/π2+1>0,f:0,1]×0,+∞)→0,+∞)是连续函数,λ>0是常数.
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| 关 键 词： | 四阶 周期边值问题 正解 多解 度理论 |
Exsitence of Mutiplicity Positive Solutions of Some Nonlinear Fourth-orderperiodic Boundary Value Problem |
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| LI Ding-shi,LIU Wen-bin,XU Cong-cong,ZHANG Wei-wei.Exsitence of Mutiplicity Positive Solutions of Some Nonlinear Fourth-orderperiodic Boundary Value Problem[J].Mathematics in Practice and Theory,2008,38(16). |
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| Authors: | LI Ding-shi LIU Wen-bin XU Cong-cong ZHANG Wei-wei |
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| Abstract: | The existence of at least two positive solutions is proved for the nonlinear fourth-order periodic boundary valve problem u(4)(t)-βu″(t)+αu(t)=λf(t,u(t)),0≤t≤1,u(i)(0)=u(i)(1),i=0,1,2,3,where β>-2π2,0<α<(1/2β+2π2)2,α/π4+β/π2+1>0,λ>0 is a constant and f:×0,+∞)→0,+∞) is continuous by using fixed-point theorem and degree theory. |
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| Keywords: | fourth-order periodic boundary value problem positive solution multiplicity degree theorem |
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