一类带积分边界条件的三阶微分方程边值问题的解

龙菲菲

(兰州理工大学理学院,甘肃兰州 730050)

一类带积分边界条件的三阶微分方程边值问题的解

龙菲菲

(兰州理工大学理学院,甘肃兰州 730050)

运用Banach压缩映射原理以及Leray-Schauder连续性原理,在非线性项为L1-Caratheodory函数的条件下,研究了一类带积分边界条件的三阶微分方程边值问题解的唯一性、存在性以及解集的紧性.

边值问题;解;唯一性;存在性;紧性

DO I：10.3969/j.issn.1008-5513.2013.04.013

1 引言

三阶微分方程起源于应用数学和物理学的许多不同领域,譬如,带有固定或变化横截面的屈曲梁的挠度、三层梁、电磁波、地球引力吹积的涨潮等.带积分边界条件的边值问题不仅包含两点及三点边值问题作为其特殊情形,而且还可以更精确地描述许多重要的现象,例如,在热传导、化学工程、地下水流、热弹性、等离子物理等领域中,对许多问题的讨论都可以归结为对带积分边界条件的边值问题的研究.目前对带积分边界条件的三阶微分方程边值问题的研究越来越多[18].特别地,2011年,文献[8]研究了Banach空间E中的三阶微分方程

下正解的存在性和不存在性,其中,f∈C([0,1]×P,P),这里,P是E中的锥.使用的主要工具是锥上的不动点定理和不动点指数理论.

2 预备引理

3 主要结果

参考文献

[1]Wang Youyu,GeWeigao.Existence of solutions for a third order dif erential equation w ith integralboundary cond itions[J].Com pu t.M ath.A pp l.,2007,53:144-154.

[2]Graef JR,Yang Bo.Solution and positive solution of a sem ilinear third-order equation[J].Discrete Contin. Dyn.Syst.Ser.S,2008,1:89-97.

[3]Graef J R,Webb J R L.Third order boundary value p rob lem s with non local boundary conditions[J]. Non linear Anal.,2009,71:1542-1551.

[4]Boucherif A,Bouguima SM,A l-Malki N,et al.Third order dif erential equationsw ith integral boundary conditions[J].Non linear Anal.,2009,71:1736-1743.

[5]Sun Jianping,Li Haibao.Monotone positive solution of non linear third-order BVP w ith integral boundary cond itions[J].Bound.Value Prob l.,2010,20:1-12.

[6]孙建平,靳存程.带积分边界条件的三阶边值问题的单调正解[J].兰州大学学报:自然科学版,2012,48:98-101.

[7]Zhang Haie,Sun Jianping.Existence and iteration ofmonotone positive solutions for third order non local BVPs involving integral cond itions[J].E lectron.J.Qual.Theory D if er.Equ.,2012,18:1-9.

[8]Zhao Jun fang,Wang Peiguang,Ge Weigao.Existence and nonexistence of positive solutions for a class of third order BVP w ith integral boundary conditions in Banach spaces[J].Commun.Nonlinear Sci.Numer. Simul.,2011,16:402-413.

[9]G ranas A,Dugund ji J.Fixed Point Theory,Sp ringer M onographs in M athem atics[M].New York:Sp ringer, 2003.

The solu tion for a class of th ird-order d if eren tial equation BVP w ith in tegral boundary cond itions

Long Feifei

(School of Science,Lanzhou University of Technology,Lanzhou 730050,China)

By using Banach contraction princip le and Leray-Schauder continuation p rincip le,the uniqueness and existence of solutions and the com pactness of solutions set are investigated for a class of third-order differential equation BVP with integral boundary conditions under the condition that the nonlinear term is an L1-Caratheodory function.

boundary value p rob lem,solution,uniqueness,existence,com pactness

O175

A

1008-5513(2013)04-0425-08

2013-04-10.

龙菲菲(1988-),硕士生,研究方向：应用微分方程.

2010 M SC:34B 15