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时标上三阶非线性p-Laplacian三点边值问题的正解 被引量：1

Positive Solutions for Third Order Nonlinearp-Laplacian Three-Point Boundary Value Problems on Time Scales
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摘要 研究了时标上三阶非线性p-Lap lac ian三点边值问题[φp(p(t)uΔ(t))]+a(t)f(t,u(t))=0,t∈[0,T],βu(0)-γuΔ(0)=0,uΔ(T)=αu(η),uΔ(0)=0借助于锥上的五泛函不动点定理,得到了边值问题至少有三个正解的一些新的结果,同时给出了例子验证了主要结果。 The following third order nonlinear p-Laplacian three-point boundary value problems on time scales [φp（p（t）u^Δ（t））] ＋a（t）f（t,u（t））=0,t∈,βu（0）-γuΔ（0）=0,u^Δ（T）=αu（η）,u^Δ（0）=0are studied.By means of five functionals fixed point theorems in cones,some new results for the existence of at least three positive solutions of the boundary value problem are obtained.As an application,an example is given to illustrate the main result.
作者 武利猛 杨军 陆海波 张娟
机构地区 华东师范大学数学系 燕山大学理学院 河北省数学研究中心
出处 《中山大学学报（自然科学版）》 CAS CSCD 北大核心 2011年第3期17-21,共5页 Acta Scientiarum Naturalium Universitatis Sunyatseni
基金 国家自然科学基金资助项目(60604004) 河北省自然科学基金数学研究专项资助项目(07M005)
关键词 时标 边值问题 正解 不动点定理 time scales boundary value problem positive solutions fixed point theorem
分类号 O175.14 [理学—基础数学]
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参考文献10

  • 1BOHNER M, PETERSON A. Dynamic equations on time scales : an introduction with applications [ M ]. Boston : Birkhauser, 2001.
  • 2BOHNER M, PETERSON A. Advances in dynamic e- quations on time scales[ M]. Boston: Birkhauser, 2003.
  • 3HONG S H. Triple positive solutions of three-point boundary value problems for p-Laplacian dynamic equa- tions on time scales [ J ]. Journal of Computational and Applied Mathematics, 2007, 206 : 967 - 976.
  • 4王培光,王颖.时间尺度上二阶动力方程三点边值问题解的存在性[J].数学学报（中文版）,2007,50(3):701-706. 被引量：8
  • 5SUN H R, LI W T. Multiple positive solutions for p- Laplacian m-point boundary value problems on time scales [ J]. Applied Mathematics and Computation, 2006, 182 : 478 - 491.
  • 6LIANG S H, ZHANG J H, WANG Z Y. The existence of three positive solutions of m point boundary value prob- lems for some dynamic equations on time scales [ J ]. Mathematical and Computer Modelling, 2009, 49:1386 - 1393.
  • 7HAN W, LIU M X. Existence and uniqueness of a non- trivial solution for a class of third-order nonlinear p-Lapla- cian m-point eigenvalue problems on time scales [ J ]. Nonlinear Analysis, 2009, 70 : 1877 - 1889.
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二级参考文献9

  • 1Kaufmann E. R., Positive solutions of a three-point boundary value problem on a time scale, Electron. J. Differential Equations, 2003, 82: 1-11.
  • 2Anderson D. R., Avery R. I., An even order three-point boundary value problem on time scales, J. Math. Anal. Appl., 2004, 291: 514-525.
  • 3Anderson D. R., Solutions to second order three-point problems on time scales, J. Diff. Eqs. Appl., 2002,8: 673-688.
  • 4Sun H. R., Li W. T., Positive solutions for nonlinear three-point boundary value problems on time scales, J. Math. Anal. Appl., 2004, 299(2): 508-524.
  • 5Sun H. R., Li W. T., Positive solutions for nonlinear m-point boundary value problems, Acta Mathematica Sinica, Chinese Series, 2006, 49(2): 369-380.
  • 6Avery R: I., Henderson J., Two positives fixed points of nonlinear operators on ordered Banach spaces, Comm. Appl. Non. Anal., 2001, 8: 27-36.
  • 7Bohner M., Peterson A., Dynamic equations on time scales: an introduction with applications, Boston: Birkhauser MA, 2001.
  • 8Bohner M., Peterson A., Advances in dynamic equations on time scales, Boston: Birkhauser, 2002.
  • 9Chyan C. J., Henderson J., Twin solutins of boundary value problems for differential equations on measure chains, J. Comput. Appl. Math., 2002, 141: 123-131.

共引文献7

同被引文献14

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二级引证文献4

中山大学学报（自然科学版）
2011年 第3期

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