一類奇異三階三點邊值問題的正解

王珍 朱少平

摘 要 利用krasnoelskii錐拉伸與壓縮不動點定理考察了一類奇異非線性三階三點邊值問題的正解的存在性，得到了此類邊值問題在奇異條件下至少存在一個正解的結(jié)果。

關(guān)鍵詞 三階三點邊值問題 奇異 正解 錐 不動點定理

中圖分類號：O175 文獻(xiàn)標(biāo)識碼：A DOI：10.16400/j.cnki.kjdks.2019.03.026

Abstract This paper is concerned with the existence of a positive solution of singular third-order three-point boundary value problem by using the Krasnoselskii's fixed point theorem of cone expansion-compression type， and established existence results for at least one positive solution for this class of problem when the nonlinear term is allowed to be singular.

Keywords third-order three-point boundary value problem； singular； positive solution； cone； fixed point theorem

參考文獻(xiàn)

[1] D.R.Anderson. Multiple positive solutions for a three-point boundary value prob- lem[J].Math Comput.Modelling，1998.27（6）：49-57.

[2] Shuhong Li. Positive solutions of nonlinear singular third-order two-point bound- ary value problem[J].2005.

[3] 劉希玉.具有奇性的一類邊值問題的正解[J].純粹數(shù)學(xué)和應(yīng)用數(shù)學(xué)，1998.1.

[4] Q. Yao.The existence and multiplicity of positive solutions for a third-order three - point boundary value problem[J].Acta Math.Appl.Sinica，2003.19：117-122.

[5] D.Guo， V.Lakshmikantham.Nonlinear Problems in Abstract Cones[M].Academic Press， San Diego，1988.

[6] Ma Ru-yun.Existence theorems for a second order three-point boundary value pro- blem[J].J Math Anal Appl，1997.212：430-442.

[7] Ma Ru-yun. Positive solutions of a nonlinear three-point boundary value problems [J].Electron. J. Differential Equations，1999.34：1-8.

[8] 郭大鈞.非線性泛函分析[M].濟(jì)南：山東科學(xué)技術(shù)出版社，2003.

[9] 孫經(jīng)先.非線性泛函分析及其應(yīng)用[M].北京：科學(xué)出版社，2007.

[10] 葛渭高.非線性常微分方程邊值問題[M].北京：科學(xué)出版社，2007.

[11] L.Guo，J.Sun，Y.Zhao. Existence of positive solutions for nonlinear third-order three-point boundary value problems[J].Nonlinear Anal.，2008.68（10）：3151 -3158.