尚仲平,金燕,魯淑霞

(1.燕山大學(xué)職業(yè)技術(shù)學(xué)院,河北秦皇島 066004;2.燕山大學(xué)理學(xué)院,河北秦皇島 066004;3.河北大學(xué)數(shù)學(xué)與計(jì)算機(jī)學(xué)院,河北保定 071002)

時(shí)標(biāo)上一階脈沖方程的周期邊值問題

尚仲平1,金燕2,魯淑霞3

(1.燕山大學(xué)職業(yè)技術(shù)學(xué)院,河北秦皇島 066004;2.燕山大學(xué)理學(xué)院,河北秦皇島 066004;3.河北大學(xué)數(shù)學(xué)與計(jì)算機(jī)學(xué)院,河北保定 071002)

針對(duì)時(shí)標(biāo)上一類一階脈沖方程的周期邊值問題,該論文基于算子不動(dòng)點(diǎn)原理、上下解方法和單調(diào)迭代技巧,給出了周期邊值問題解存在性的充分條件,并舉例加以驗(yàn)證了主要結(jié)果.

時(shí)標(biāo);周期邊值問題;脈沖方程;上下解方法;單調(diào)迭代技巧

MSC 2010:34K10;34B37;34B15

近年來,關(guān)于脈沖方程的周期邊值問題的討論備受廣大學(xué)者的關(guān)注,但是在以往的研究過程中,大多是對(duì)微分方程的討論,而針對(duì)時(shí)標(biāo)上的一階動(dòng)力系統(tǒng)的討論甚少[1-2],本文考慮如下時(shí)標(biāo)上一階脈沖方程

文中所用時(shí)標(biāo)上的相關(guān)知識(shí)見文獻(xiàn)[3],在此不再詳述.記

1 引理

2 線性問題的解的存在性結(jié)果

3 主要結(jié)果

4 舉例

[1]GENG Fengjie,XU Yancong,ZHU Deming.Periodic boundary value p roblems fo r first-order impulsive dynamic equations on time scales[J].Nonlinear Analysis,2008,69：4074-4087.

[2]WANGDabin.Positive solutions for nonlinear first-order periodic boundary value p roblem sof impulsive dynamic equations on time scales[J].Computers and Mathematics w ith Applications,2008,56：1496-1504.

[3]MARTIN Bohner,ALLAN Peterson.Dynamic equations on time scales,an introduction w ith app lications[M].Boston：Birkhauser,2001.

[4]LUO Zhiguo,JING Zhujun.Periodic boundary value p roblem fo r first-o rder impulsive functional differential equations[J].Computers and Mathematics w ith App lications,2008,55：2094-2107.

[5]李云紅,呂文靜,郭彥平.測(cè)度鏈上二階邊值問題多個(gè)正解的存在性[J].河北大學(xué)學(xué)報(bào)：自然科學(xué)版,2008,28(5)：462-465.

Periodic Boundary Value Problem for First-order Impulsive Functional Dynam ic Equations

SHANG Zhong-ping1,JIN Yan2,LU Shu-xia3
(1.Vocational and Technical College,Yanshan University,Qinhuangdao 066004,China;2.College of Science,Yanshan University,Qinhuangdao 066004,China;3.College of Mathematics and Computer Science,Hebei University,Baoding 071002,China)

Based on the know ledge of operato r fixed points,the upper and low er solution method and the monotone iterative technique,this paper p resents some sufficient conditions for the existence of the periodic boundary value p roblem fo r first-o rder impulsive functional dynamic equations on time scales,an examp le is also given to illustrate the main results.

time scales;Periodic boundary value p roblem;impulsive equations;lower and upper solution method;monotone iterative technique

O 175

A

1000-1565(2011)04-341-07

2010-12-05

河北省自然科學(xué)基金項(xiàng)目(F2011201063);河北省教育廳科學(xué)技術(shù)研究計(jì)劃(2009107)

尚仲平(1964-),男,河北邯鄲人,燕山大學(xué)講師,主要從事微分方程理論的研究.

E-mail：shangzhongping1@163.com

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