完全三阶边值问题解的存在性
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摘要
本文讨论了如下完全三阶两点边值问题{-u(t)=f(t,u(t),u′(t),u″(t)),t∈[0,1],u(0)=u′(0)=u″(1)=0解的存在性,其中f:[0,1]×R3→R为连续函数.当f(t,x,y,z)满足关于x,y,z超线性增长的不等式条件及f(t,x,y,z)关于z满足Nagumo型增长条件时,本文应用Leray-Schauder不动点定理获得了该问题解的存在性.
In this paper,the existence of solutions of the following fully third order boundary value problem{-u(t) =f(t,u(t),u′(t),u″(t)),t∈ [0,1],u(0)=u′(0)=u″(1)=0is considered,where f:[0,1]×R3→ Ris continuous.Applying the Leray-Schauder fixed point theorem,the existence of solutions is obtained under the conditions that f(t,x,y,z)satisfies an inequility condition that allows f(t,x,y,z)superlinear growth and f(t,x,y,z)satisfies the Nagumo-type growth condition on z.
In this paper,the existence of solutions of the following fully third order boundary value problem{-u(t) =f(t,u(t),u′(t),u″(t)),t∈ [0,1],u(0)=u′(0)=u″(1)=0is considered,where f:[0,1]×R3→ Ris continuous.Applying the Leray-Schauder fixed point theorem,the existence of solutions is obtained under the conditions that f(t,x,y,z)satisfies an inequility condition that allows f(t,x,y,z)superlinear growth and f(t,x,y,z)satisfies the Nagumo-type growth condition on z.
引文
[1]Li S H.Positive solutions of nonlinear singular third-order two-point boundary value problem[J].J Math Anal Appl,2006,323:413.
[2]Sun Y P.Positive solutions of singular third-order threepoint boundary value problem[J].J Math Anal Appl,2005,306:589.
[3]Grossinho M D R,Minhos F M.Existence result for some third order separated boundary value problems[J].Nonlinear Anal-Theor,2001,47:2407.
[4]Cabada A.The method of lower and upper solutions for second,third,forth,and higher order boundary value problem[J].J Math Anal Appl,1994,185:302.
[5]Du Z J,Ge W G,Lin X J.Existence of solutions for a class of third-order nonlinear boundary value problems[J].J Math Anal Appl,2004,294:104.
[6]Hopkins B,Kosmatov N.Third-order boundary value problems with sign-changing solutions[J].Nonlinear Anal-Theor,2007,67:126.
[7]Yao Q L,Feng Y Q.The existence of solutions for a third-order two-point boundary value problem[J].Appl Math Lett,2002,15:227.
[8]张宏旺,李永祥.一类非线性三阶边值问题的单调迭代方法[J].西南大学学报:自然科学版,2009,31:34.
[9]Feng Y Q,Liu S Y.Solvability of a third-order twopoint boundary value problem[J].Appl Math Lett,2005,18:1034.
[10]姚庆六.线性增长限制下一类三阶边值问题的可解性[J].纯粹数学与应用数学,2005,21:164.
[11]李涛涛.非线性三点边值问题正解的存在性[J].四川大学学报:自然科学版,2017,54:683.
[12]葛渭高,郭玉芝.三阶非线性常微分方程两点边值问题解的存在性[J].系统科学与数学,1996,16:181.
[13]Sun Y P,Zhao M,Li S H.Monotone positive solution of nonlinear third-order two-point boundary value problem[J].Miskolc Math Notes,2014,15:743.
[2]Sun Y P.Positive solutions of singular third-order threepoint boundary value problem[J].J Math Anal Appl,2005,306:589.
[3]Grossinho M D R,Minhos F M.Existence result for some third order separated boundary value problems[J].Nonlinear Anal-Theor,2001,47:2407.
[4]Cabada A.The method of lower and upper solutions for second,third,forth,and higher order boundary value problem[J].J Math Anal Appl,1994,185:302.
[5]Du Z J,Ge W G,Lin X J.Existence of solutions for a class of third-order nonlinear boundary value problems[J].J Math Anal Appl,2004,294:104.
[6]Hopkins B,Kosmatov N.Third-order boundary value problems with sign-changing solutions[J].Nonlinear Anal-Theor,2007,67:126.
[7]Yao Q L,Feng Y Q.The existence of solutions for a third-order two-point boundary value problem[J].Appl Math Lett,2002,15:227.
[8]张宏旺,李永祥.一类非线性三阶边值问题的单调迭代方法[J].西南大学学报:自然科学版,2009,31:34.
[9]Feng Y Q,Liu S Y.Solvability of a third-order twopoint boundary value problem[J].Appl Math Lett,2005,18:1034.
[10]姚庆六.线性增长限制下一类三阶边值问题的可解性[J].纯粹数学与应用数学,2005,21:164.
[11]李涛涛.非线性三点边值问题正解的存在性[J].四川大学学报:自然科学版,2017,54:683.
[12]葛渭高,郭玉芝.三阶非线性常微分方程两点边值问题解的存在性[J].系统科学与数学,1996,16:181.
[13]Sun Y P,Zhao M,Li S H.Monotone positive solution of nonlinear third-order two-point boundary value problem[J].Miskolc Math Notes,2014,15:743.