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测度链上p-Laplacian 边值问题的三个正对称解
引用本文:苏有慧,李万同.测度链上p-Laplacian 边值问题的三个正对称解[J].数学物理学报(A辑),2008,28(6):1232-1241.
作者姓名:苏有慧  李万同
作者单位:(1.徐州工程学院数理学院 徐州 221008; 2.兰州大学数学与统计学院 兰州 730000)
基金项目:国家自然科学基金(10571078)和教育部高等学校教学科研奖励计划资助
摘    要:该文研究了p-Laplacian 动力边值问题 (g(u(t)))+a(t)f(t, u(t))=0, t ∈ 0, T] T, u(0)=u(T)=w, u(0)=-u(T) 正解的存在性. 其中w是非负实数, g(ν)=|ν| p-2ν, p>1 . 根据对称技巧和五泛函不动点定理, 证明了边值问题至少有三个正的对称解, 同时, 给出了一个例子验证了我们的结果.

关 键 词:测度链  边值问题  正对称解  p-Laplacian  不动点定理.
收稿时间:2006-12-05
修稿时间:2008-05-11

Triple Positive Symmetric Solutions of Two-Point BVPs for p-Laplacian Dynamic Equations on Time Scales
Su Youhui,Li Wantong.Triple Positive Symmetric Solutions of Two-Point BVPs for p-Laplacian Dynamic Equations on Time Scales[J].Acta Mathematica Scientia,2008,28(6):1232-1241.
Authors:Su Youhui  Li Wantong
Institution:(1.Mathematics and Physical Sciences Technology, Xuzhou Institute of Technology, Xuzhou 221008; 2.School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000)
Abstract:This paper is concerned with the p-Laplacian boundary value problem (g(u(t)))+a(t)f(t, u(t))=0 for t ∈ 0, T]T, u(0)=u(T)=w, u(0)=-u(T), where w is anonnegative real number and g(ν)=lν|p-2ν with p>1 . By using symmetry technique and a five functionals fixed-point theorem, we prove that the boundary value problem has at least three positive symmetric solutions. As application, an example is given to illustrate our result.
Keywords:p-Laplacian
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