帶變號(hào)G reen函數(shù)的三階三點(diǎn)邊值問(wèn)題的正解

張富娟

(蘭州理工大學(xué)理學(xué)院,甘肅蘭州 730050)

帶變號(hào)G reen函數(shù)的三階三點(diǎn)邊值問(wèn)題的正解

張富娟

(蘭州理工大學(xué)理學(xué)院,甘肅蘭州 730050)

運(yùn)用Guo-K rasnoselskii不動(dòng)點(diǎn)定理,在相應(yīng)的Green函數(shù)變號(hào)的情況下,建立了三階常微分方程三點(diǎn)邊值問(wèn)題至少存在兩個(gè)正解的若干存在性準(zhǔn)則.

三階三點(diǎn)邊值問(wèn)題;正解;存在性;錐;變號(hào)Green函數(shù)

DO I：10.3969/j.issn.1008-5513.2013.05.015

1 引言

2 預(yù)備知識(shí)

3 主要結(jié)果

參考文獻(xiàn)

[1]G regus M.Third O rder Linear Dif erential Equations[M].Reidel:Dord recht,1987.

[2]Anderson D R.Green′s function for a third-order generalized right focal p rob lem[J].J.Math.Anal.App l., 2003,288(1):1-14.

[3]Sun Y.Positive solutions of singular third-order three-point boundary value problem[J].J.Math.Anal. A pp l.,2005,306(2):589-603.

[4]Guo L J,Sun J P,Zhao Y H.Existence of positive solution for non linear third-order three-point boundary value problem[J].Nonlinear Anal.,2008,68(10):3151-3158.

[5]Palam ides A P,Stavrakak is N M.Existence and uniquenessof a positive solu tion for a third-order three-poin t boundary value p rob lem[J].Electron.J.Dif erential Equations,2010,155:1-12.

[6]Prasad K R,Narayana N V V S S.Solvability of a non linear third-order three-point general eigenvalue p rob lem on time scales[J].Electron.J.Dif erential Equations,2010,57:1-12.

[7]Sun Y.Positive solu tions for third-order th ree-point nonhom ogeneous boundary value prob lem s[J].App l. M ath.Lett.,2009,22(1):45-51.

[8]Palam ides A P,Sm yrlis G.Positive solutions to a singular third-order three-point boundary value prob lem w ith indef nitely signed Green′s function[J].Nonlinear Anal.,2008,68(7):2104-2118.

[9]Sun J P,Zhao J.Positive solution for a third-order th ree-point boundary value p rob lem w ith sign-changing Green′s function[J].Commun.Appl.Anal.,2012,16(2):219-228.

[10]Sun J P,Zhao J.M ultip le positive solutions for a third-order three-point boundary value p rob lem w ith sign-changing G reen′s function[J].E lectron.J.Dif erential Equations,2012,118:1-7.

Positive so lu tions for a th ird-order th ree-point boundary value p rob lem w ith sign-changing G reen′s function

Zhang Fujuan

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

By using the Guo-K rasnoselskii fxed-point theorem,some existence criteria of at least two positive solutions are established for a three-point boundary value p rob lem of third-order ordinary dif erential equation under the condition that the corresponding Green′s function is sign-changing.

third-order th ree-point boundary value prob lem,positive solu tion,existence,cone, sign-changing G reen′s function

O175

A

1008-5513(2013)05-0544-07

2013-07-16.

張富娟(1986-),碩士生,研究方向：應(yīng)用微分方程.

2010 MSC:34B15