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应用数学学报  2014, Vol. 37 Issue (2): 234-246    DOI:
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一类泛函微分方程正周期解的存在性和多解性
景兰1, 莫宜春2
1. 兰州职业技术学院, 兰州 730070;
2. 西北师范大学, 兰州 730070
Existence and Multiplicity of Positive Periodic Solutions for a Class of Functional Differential Equations
JING Lan1, MO Yichun2
1. Lanzhou Vocational Technical College, Lanzhou 730070;
2. Department of Mathematics, Northwest Normal University, Lanzhou 730070
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摘要 本文运用上下解方法和不动点指数理论研究了一类泛函微分方程正周期解的存在性、多解性及不存在性. 当参数在不同范围内取值时,建立了方程正周期解的存在性、多解性和不存在性结果.
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景兰
莫宜春
关键词泛函微分方程   正周期解   不动点指数   存在性   时滞     
Abstract: In this paper, by using the fixed point index theory and lower and upper solutions method, we are concerned with the existence, multiplicity and nonexistence of positive periodic solutions for a kind of functional differential equation. The existence, multiplicity and nonexistence results are established in terms of different value of parameters.
Key wordsfunctional differential equations   positive periodic solutions   fixed point index   existence   delays   
收稿日期: 2012-05-14;
基金资助:国家自然科学基金(No.11061030),高等学校博士学科点专项科研基金(No.20126203110004),甘肃省自然科学基金(No.1208RJZA258)资助项目.
引用本文:   
景兰,莫宜春. 一类泛函微分方程正周期解的存在性和多解性[J]. 应用数学学报, 2014, 37(2): 234-246.
JING Lan,MO Yichun. Existence and Multiplicity of Positive Periodic Solutions for a Class of Functional Differential Equations[J]. Acta Mathematicae Applicatae Sinica, 2014, 37(2): 234-246.
 
[1] Gopalsamy K, Weng P X. Global Attractivity and Level Crossing in Model of Haematopoiesis. Bull. Inst. Math. Acad. Sinica, 1994, 22(4): 341-360
[2] Wan A, Jiang D Q. Existence of Positive Periodic Solutions for Functional Differential Equations. Kyushu J. Math., 2002, 56: 193-202
[3] Joseph W, So H, Yu J S. Global Attractivity and Uniform Persistence in Nicholson's Blowflies. Differential Equation and Dynam. Systems, 1994, 2(1): 11-18
[4] Weng P X. Existence and Global Attractivity of Periodic Solution of Integro-differential Equation in Population Dynamics. Acta. Appl. Math., 1996, 12(4): 427-434
[5] Zhang G, Cheng S S. Positive Periodic Solutions of Nonautonomous Functional Differential Equations Depending on a Parameter. Abstract Appl. Anal., 2002, 7: 279-286
[6] Wu Y H. Existence of Positive Periodic Solutions for a Functional Differential Equation with a Parameter. Nonlinear Anal., 2008, 68: 1954-1962
[7] Cheng S S, Zhang G. Existence of Positive Periodic Solutions for Non-autonomous Functional Differential Equations. Electron J. Differential Equations, 2001, 59: 1-8
[8] Padhi S, Shilpee S. Multiple Periodic Solutions for Nonlinear First Order Functional Differential Equations with Applications to Population Dynamics. Appl. Math. Comput., 2008, 203(1): 1-6
[9] Ma R Y, Chen R P, Chen T L. Existence of Positive Periodic Solutions of Nonlinear First-order Delayed Differential Equations. J. Math. Anal. Appl., 2011, 384: 527-535
[10] He T S, Yang F J, Chen C Y, Peng S G. Existence and Multiplicity of Positive Solutions for Nonlinear Boundary Value Problems with a Parameter. Comput. Math. Appl., 2011, 53: 3355-3363
[11] Graef J R, Kong L J. Existence of Multiple Periodic Solutions for First Order Functional Differential Equations. Math. Comput. Model., 2011, 54: 2968-2962
[12] Yu J S, Xiao H F. Multiple Periodic Solutions with Minimal Period 4 of the Delay Differential Equation x'(t)=-f(t, x(t-1)). J. Differential Equations, 2013, 254: 2158-2172
[13] Ma R Y, Yang B X, Wang Z Y. Positive periodic solutions of first-order delay differential equations with impulses. Appl. Math. Comput., 2013, 219: 6074-6083
[14] 郭大钧. 非线性泛函分析. 济南: 山东科学技术出版社, 1985 (Guo D J. Nonlinear Functional Analysis. Jinan: Shandong Science and Technology Publishing House, 1985)
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