一類帶積分邊界條件的三階微分方程邊值問題的解

龍菲菲

(蘭州理工大學(xué)理學(xué)院,甘肅蘭州 730050)

一類帶積分邊界條件的三階微分方程邊值問題的解

龍菲菲

(蘭州理工大學(xué)理學(xué)院,甘肅蘭州 730050)

運(yùn)用Banach壓縮映射原理以及Leray-Schauder連續(xù)性原理,在非線性項(xiàng)為L1-Caratheodory函數(shù)的條件下,研究了一類帶積分邊界條件的三階微分方程邊值問題解的唯一性、存在性以及解集的緊性.

邊值問題;解;唯一性;存在性;緊性

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

1 引言

三階微分方程起源于應(yīng)用數(shù)學(xué)和物理學(xué)的許多不同領(lǐng)域,譬如,帶有固定或變化橫截面的屈曲梁的撓度、三層梁、電磁波、地球引力吹積的漲潮等.帶積分邊界條件的邊值問題不僅包含兩點(diǎn)及三點(diǎn)邊值問題作為其特殊情形,而且還可以更精確地描述許多重要的現(xiàn)象,例如,在熱傳導(dǎo)、化學(xué)工程、地下水流、熱彈性、等離子物理等領(lǐng)域中,對(duì)許多問題的討論都可以歸結(jié)為對(duì)帶積分邊界條件的邊值問題的研究.目前對(duì)帶積分邊界條件的三階微分方程邊值問題的研究越來越多[18].特別地,2011年,文獻(xiàn)[8]研究了Banach空間E中的三階微分方程

下正解的存在性和不存在性,其中,f∈C([0,1]×P,P),這里,P是E中的錐.使用的主要工具是錐上的不動(dòng)點(diǎn)定理和不動(dòng)點(diǎn)指數(shù)理論.

2 預(yù)備引理

3 主要結(jié)果

參考文獻(xiàn)

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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.

龍菲菲(1988-),碩士生,研究方向：應(yīng)用微分方程.

2010 M SC:34B 15