| 一类四阶常微分方程周期边值问题的正解 |
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| 引用本文： | 王天祥,李永祥. 一类四阶常微分方程周期边值问题的正解[J]. 数学杂志, 2021, 0(2): 141-150 |
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| 作者姓名： | 王天祥 李永祥 |
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| 作者单位： | 西北师范大学数学与统计学院 |
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| 基金项目： | 国家自然科学基金基金资助(11661071)。 |
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| 摘 要： | 本文研究了四阶周期边值问题{u4(t)-βu″(t)+αu(t)=f(t,u(t),u′(t),u″(t),u′′′(t)),t∈[0,1],ui(0)=ui(1),i=0,1,2,3正解的存在性,其中f:[0,1]×[0,+∞)×R3→[0,+∞)连续.利用锥上的不动点指数理论,获得了该问题正解的存在性结果,推广了已有文献的相关结果.
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| 关 键 词： | 四阶常微分方程 正解 锥 不动点指数理论 |
POSITIVE SOLUTIONS OF PERIODIC BOUNDARY VALUE PROBLEMS FOR A CLASS OF FOURTH ORDER ORDINARY DIFFERENTIAL EQUATIONS |
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| WANG Tian-xiang,LI Yong-xiang. POSITIVE SOLUTIONS OF PERIODIC BOUNDARY VALUE PROBLEMS FOR A CLASS OF FOURTH ORDER ORDINARY DIFFERENTIAL EQUATIONS[J]. Journal of Mathematics, 2021, 0(2): 141-150 |
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| Authors: | WANG Tian-xiang LI Yong-xiang |
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| Affiliation: | (College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China) |
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| Abstract: | In this paper,we discuss the existence of positive solution for the fourth-order periodic boundary value problem {u4(t)-βu″(t)+αu(t)=f(t,u(t),u′(t),u″(t),u′′′(t)),t∈[0,1],ui(0)=ui(1),i=0,1,2,3 where f:[0,1]×[0,+∞)×R3→[0,+∞)continuous.By using the fixed point index theory on cone,the existence of positive solution is obtained,and extends some related conclusions on this topic. |
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| Keywords: | fourth-order ordinary differential equations positive solution cone fixed point index theory |
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