测度链上二阶边值问题多个正解的存在性

  • 李云红 ,
  • 吕文静 ,
  • 郭彦平
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  • 1.河北科技大学,理学院,河北,石家庄,050018; 2.河北大学,新校区建设办公室,河北,保定,071002

网络出版日期: 2008-09-25

基金资助

河北省自然科学基金

Existence of Multiple Positive Solutions for A Second-order Boundary Value Problem on A Measure Chain

  • LI Yun-hong ,
  • LU Wen-jing ,
  • GUO Yang-ping
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Online published: 2008-09-25

摘要

讨论测度链上二阶边值问题,xΔΔ+k(t)f(t,x(σ(t)))=0,t∈[t1,t2],αx(t1)-βxΔ(t1)=0,γx(σ(t2))+δxΔ(σ(t2))=0正解的存在性,[t1,t2]T,T是测度链,利用Leggett-Williams不动点定理,可得该问题至少存在3个正解.

本文引用格式

李云红 , 吕文静 , 郭彦平 . 测度链上二阶边值问题多个正解的存在性[J]. 河北大学学报(自然科学版), 2008 , 28(5) : 462 -465 . DOI: 10.3969/j.issn.1000-1565.2008.05.005

参考文献

[1] 杜增吉, 葛渭高, DU ZENGJI, GE WEIGAO. 二阶测度链上Sturm-Liouville型边值问题的多个正解存在性 [J]. 应用数学学报 2006.doi:10.3321/j.issn:0254-3079.2006.01.016
[2] HILGER S. Analysis on measure chains-a unified approach to continuous and discrete calculus [J]. Results in Mathematics 1990, 18.
[3] ERBE L H, PETERSON A C. Positive solutions for a nonlinear differential equation on a measure chain [J]. Mathematical and Computer Modelling 2000, 32.
[4] Douglas R. Anderson. Eigenvalue intervals for a two-point boundary value problem on a measure chain [J]. Journal of Computational and Applied Mathematics 2002, 1/2(1/2).
[5] F. Merdivenci Atici, G. Sh. Guseinov. On Green's functions and positive solutions for boundary value problems on time scales [J]. Journal of Computational and Applied Mathematics 2002, 1/2(1/2).
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