全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用：99美元
投递稿件

查看量下载量

相关文章

更多...

四阶时滞微分方程边值问题的正解

, PP. 172-177

Keywords: 四阶时滞微分方程,边值问题,正解,锥上的不动点指数理论

Full-Text   Cite this paper   Add to My Lib

Abstract:

随着泛函微分方程理论的发展以及其在物理、力学、自动控制理论、生物学、经济学等众多学科中的应用,时滞微分方程边值问题成为关注的一个热点.运用锥上的不动点指数理论研究了四阶时滞微分方程边值问题u(4)(t)+au″(t)-bu(t)=f(t,ut),t∈［0,1］,u(t)=(t),t∈［-τ,0］,u(0)=u(1)=u″(0)=u″(1)=0正解的存在性,其中,f［0,1］×C+［0,+∞)连续,C+={φ∈C|φ(θ)≥0,θ∈［-τ,0］},(t)∈C(［-τ,0］,［0,+∞)),(0)=0,对t∈［0,1］,ut(θ)=u(t+θ),θ∈［-τ,0］,0≤τ-a24,bπ4+aπ2<1.所得结果推广和改进了现有结果.

 References

[1]  Berezansky L, Diblík J. Positive solutions of second-order delay differential equations with a damping term[J]. Comput Math Appl,2010,60:1332-1342.
[2]  Li Y. A monotone iterative technique for solving the bending elastic beam equations[J]. Appl Math Comput,2010,217:2200-2208.
[3]  Yang B, Ma R, Gao C. Positive periodic solutions of delayed differential equations[J]. Appl Math Comput,2011,218(8):4538-4545.
[4]  Li Y. Positive periodic solutions of second-order differential equations with delays[J/OL]. Abst Appl Anal,2012:2012,ID829783:13. http://www.hindawi.com/journals/aaa/2012/829783.
[5]  Li Q, Li Y. On the existence of positive periodic solutions for second-order functional differential equations with multiple delays[J/OL]. Abst Appl Anal,2012:2012,ID929870:13. http://www.hindawi.com/journals/aaa/2012/929870.
[6]  郭大钧,孙经先. 抽象空间常微分方程[M]. 济南:山东科学技术出版社,1989.
[7]  郭大钧. 非线性泛函分析[M]. 济南:山东科学技术出版社,2002:314-315.
[8]  [１] Gupta C P. Existence and uniqueness results for the bending of an elastic beam equation at resonance[J]. J Math Anal Appl,1988,135:208-225.
[9]  Gupta C P. Existence and uniqueness theorems for a bending of an elastic beam equation[J]. Appl Anal,1988,26:289-304.
[10]  Li Y. Positive solutions of fourth-order boundary value problems with two parameters[J]. J Math Anal Appl,2003,281:477-484.
[11]  李永祥. 四阶非线性边值问题解的存在性与上下解方法[J]. 数学物理学报,2003,A23(2):245-252.
[12]  李永祥,杨和. 用椭圆描述的四阶边值问题的两参数非共振条件[J]. 数学物理学报,2010,A30(1):239-244.
[13]  黄永峰. 一类带参数的四阶两点边值问题正解的存在性[J]. 长江大学学报:自然科学版,2011,8(9):1-3.
[14]  王珍燕. 带2个参数四阶边值问题的正解及多个正解的存在性[J]. 烟台大学学报:自然科学版,2012,25(1):9-15.
[15]  Ma R. Existence of positive solutions of a fourth-order boundary value problem[J]. Appl Math Comput,2005,168:1219-1231.
[16]  Ma R. Positive solutions for boundary value problems of functional differential equations[J]. Appl Math Comput,2007,193:66-72.
[17]  [１ Pang C C, Dong W, Wei Z L. Multiple soluttions for fourth-order boundary value problem[J]. J Math Anal Appl,2006,314:464-476.
[18]  [１ Jiang D, Liu H, Xu X. Nonresonant singgular fourth-order boundary value problems[J]. Appl Math Lett,2005,18:69-75.
[19]  [１ 宋利梅,翁佩萱. 四阶泛函微分方程边值问题正解的存在性[J]. 高校应用数学学报,2011,26(1):67-77.
[20]  [１ 宋常修,翁佩萱. 四阶非线性泛函微分方程边值问题的正解[J]. 华南理工大学学报:自然科学版,2006,34(7):128-132.
[21]  [１ 夏青. 一类二阶时滞微分方程的边值问题[J]. 中国海洋大学学报,2007,20:127-130.
[22]  [１ 王洁,刘斌. 二阶时滞微分方程边值问题正解的存在性[J]. 应用数学,2007,20:127-130.
[23]  [１ 王宏洲. 二阶时滞微分方程边值问题的上下解方法[J]. 数学学报,2010,53(3):489-494.
[24]  [１ Weng P. Monotone method for fourth-order boundary value problems of functional differential equations[J]. Comput Math Appl,1993,37:1-9.
[25]  [１ Weng P, Jiang D. Existence of positive solutions for boundary value problem of second-order FDE[J]. Nonlinear Anal,2008,68:3646-3656.
[26]  [１ Bai D, Xu Y. Positive solutions and eigenvalue intervals of nonlocal boundary value problems with delays[J]. J Math Anal Appl,2007,334:1152-1166.
[27]  Gao C, Cuo Z. Existence of multiple periodic solutions foer a class of second-order delay differential equations[J]. Nonlinear Anal,2009,10(5):3285-3297.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133