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山东大学学报(理学版) ›› 2016, Vol. 51 ›› Issue (4): 49-52.doi: 10.6040/j.issn.1671-9352.0.2015.308

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共振条件下的二阶多点边值问题解的存在性和多解性

陈彬,Abuelgasimalshaby Elzebir   

  1. 西北师范大学数学与统计学院, 甘肃 兰州 730070
  • 收稿日期:2015-06-29 出版日期:2016-04-20 发布日期:2016-04-08
  • 作者简介:陈彬(1992— ), 女, 硕士研究生, 研究方向为常微分方程边值问题. E-mail:cb1221218@163.com
  • 基金资助:
    国家自然科学基金资助项目(10671158);甘肃省自然科学基金资助项目(3ZS051-A25-016)

Existence and multiplicity results for a second-order multi-point boundary value problem at resonance

CHEN Bin, Abuelgasimalshaby Elzebir   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2015-06-29 Online:2016-04-20 Published:2016-04-08

摘要: 在共振条件∑mk=1ak=1下, 运用紧向量场方程的解集连通理论对二阶多点边值问题u″(t)=f(t,u(t))+e(t), t∈[0,1],u'(0)=0, u(1)=∑mk=1aku(ηk)建立了解的存在性和多解性结果。其中, f:[0,1]×R→R连续, e∈C([0,1],R), 0<η12<…<ηm<1, ak>0(k=1,2,…,m)。

关键词: 解的存在性, 解集连通理论, 共振, 多解性, 多点边值问题

Abstract: It is investigated that the existence and multiplicity results for a second-order multi-point boundary value problem at resonanceu″(t)=f(t,u(t))+e(t), t∈[0,1],u'(0)=0, u(1)=∑mk=1aku(ηk)by the connectivity properties of solution set of parameterized families of compact vector fields. where f:[0,1]×R→R is continuous, e∈C([0,1],R), 0<η12<…<ηm<1, ak>0(k=1,2,…,m).

Key words: existence of solutions, multiplicity results, at resonance, connectivity properties of solution set, multi-point boundary value problem

中图分类号: 

  • O175.8
[1] IlIN V, MOISEEV E. Non-local boundary value problem of the first kind for a Sturm-Liouville operator in itsdifferential andfinite difference aspects[J]. Differential Equations, 1987, 23(7):803-810.
[2] MA Ruyun. Positive solutions a nonlinear three-point boundary value problem[J]. Electronic Journal of Differential Equations, 1999, 34:1-8.
[3] ZHANG Guang, CHENG Suisun. Positions of m-point boundary value problems[J]. Journal of Mathematical Analysis and Applications, 2004, 291(1):406-418.
[4] ZHANG Guang, CHENG Suisun. Multiple positive solutions of singular second-order m-point boundary value problems[J]. Journal of Mathematical Analysis and Applications, 2006, 317(1):442-447.
[5] KARAKOSTAS G, TSAMATOS P. On a nonlocal boundary value problem[J]. Journal of Mathematical Analysis and Applications, 2001, 259(1):209-218.
[6] 马如云. 非线性常微分方程非局部问题[M]. 北京: 科学出版社, 2004. MA Ruyun. Nonlocal problems of nonlinear ordinary differential equations[M]. Beijing: Science Press, 2004.
[7] HAN Xiaoling. Positive solutions a three-point boundary value problem at resonance[J]. Journal of Mathematical Analysis and Applications, 2007, 336(1):556-568.
[8] MA Ruyun. Existence results of a m-point boundary value problem at resonance[J]. Journal of Mathematical Analysis and Applications, 2004, 294(1):147-157.
[9] MA Ruyun. Nonlinear discrete Sturm—Liouville problems at resonance[J]. Nonlinear Analysis, 2007, 67(11):3050-3057.
[10] MARIA A D, ROSANA R. Multipoint boundary value problems of Neumann type for functional differential equations[J]. Nonlinear Analysis, 2012 13(4):1662-1675.
[11] MOHAMED M, THOMPSON B, JUSOH M S. First-order three-point boundary value problems at resonance[J]. Journal of Computational and Applied Mathematics, 2011, 235(16):4796-4801.
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