王珍 朱少平

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

關(guān)鍵詞 三階三點(diǎn)邊值問(wèn)題 奇異 正解 錐 不動(dòng)點(diǎn)定理

中圖分類(lèi)號(hào)：O175 文獻(xiàn)標(biāo)識(shí)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(lèi)邊值問(wèn)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(wèn)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.