| 拟线性二阶方程三点边值问题对称正解的存在性 |
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| 引用本文： | 李圆晓,魏英杰,高文杰.拟线性二阶方程三点边值问题对称正解的存在性[J].吉林大学学报(理学版),2010,48(1):1-8. |
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| 作者姓名： | 李圆晓 魏英杰 高文杰 |
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| 作者单位： | 吉林大学 数学研究所, 长春 130012 |
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| 基金项目： | 国家自然科学基金(批准号:10771085);;吉林大学“985工程”项目基金 |
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| 摘 要： | 研究一维p-Laplace方程(p(u′(t)))′+q(t)f(t,u(t),u′(t))=0关于三点边值u(t)=u(1-t),u′(0)-u′(1)=u(1/2)对称正解的存在性.利用Avery-Peterson不动点定理得出该问题在一定的条件下至少存在3个对称正解及在f的适当假设下至少存在2n+1个对称正解.
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| 关 键 词： | p-Laplace方程 对称正解 三点边值问题 Avery-Peterson不动点定理 |
| 收稿时间： | 2009-05-31 |
Existence of Symmetric Positive Solutions to Three-Point Boundary Value Problem of Quasilinear Second Order Equation |
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| LI Yuan-xiao,WEI Ying-jie,GAO Wen-jie.Existence of Symmetric Positive Solutions to Three-Point Boundary Value Problem of Quasilinear Second Order Equation[J].Journal of Jilin University: Sci Ed,2010,48(1):1-8. |
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| Authors: | LI Yuan-xiao WEI Ying-jie GAO Wen-jie |
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| Institution: | Institute of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | One dimension p-Laplace equation (φ_p(u'(t)))'+q(t)f(t,u(t),u'(t))=0 with boundary value conditions u(t)=u(1-t), u'(0)-u'(1)=u(1/2) was studied. Under certain conditions the above problem has at least three symmetric positive solutions shown by virtue of the Avery-Peterson fixed-point theorem and at least 2n+1 symmetric positive solutions if the function f satisfies some additional conditions. |
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| Keywords: | p-Laplace equation symmetric positive solution three-point boundary value problem Avery-Peterson fixed-point theorem |
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