带参数的一阶周期边值问题正解的全局结构
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摘要
本文运用Dancer全局分歧定理研究了带参数的一阶周期边值问题■正解的全局结构,获得了正解存在的最优区间.其中r为正参数,f∈C(R,R),a∈C([0,1],[0,∞)),且a(t)在[0,1]的任意子区间内不恒为0.
In this paper, we use Dancer's global bifurcation theorem to study the global structure of positive solutions for the following first-order periodic boundary value problem with parameter: ■where r is a positive parameter, f∈C(R,R),a∈C([0,1],[0,∞)), and a(t) is not identically equal to zero on any subinterval of [0,1]. We obtain the optimal interval for the existence of positive solutions.
In this paper, we use Dancer's global bifurcation theorem to study the global structure of positive solutions for the following first-order periodic boundary value problem with parameter: ■where r is a positive parameter, f∈C(R,R),a∈C([0,1],[0,∞)), and a(t) is not identically equal to zero on any subinterval of [0,1]. We obtain the optimal interval for the existence of positive solutions.
引文
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[3] Ruyun M,Jia X.Bifurcation from interval and positive solutions for second-order periodic boundary value problems [J].Dynam Systems Appl,2010,19:211.
[4] Tian J F,Wang W L,Cheng W S.Periodic boundary value problems for first-order impulsive difference equations with time delay [J].Adv Differ Equ,2018,79:2.
[5] Wen G,Shuanghong M,Dabin W.Periodic boundary value problems for first-order difference equations [J].Electron J Qual Theo,2012,52:39.
[6] Wang Z Y,Gao C H.Bifurcation from infinity and multiple solutions for first-order periodic boundary value problems [J].Electron J Differ Equ,2011,141:34.
[7] Ma R Y,Liu Y Q.One-signed periodic solutions of first-order functional differential equations with a parameter [J].Abstr Appl Anal,2011,11:249.
[8] Yuji L.Positive solutions of periodic boundary value problems for nonlinear first-order impulsive differential equations [J].Nonlinear Anal Theor,2009,5:2106.
[9] Tisdell Christopher C.Existence of solutions to first-order periodic boundary value problems [J].J Math Anal Appl,2006,323:1325.
[10] Gurney W S,Blythe S P,Nisbet R N.Nicholson's blowflies revisited [J].Nature,1980,187:17.
[11] Chenghua G,Fei Z,Ruyun M.Existence of positive solutions of second-order periodic boundary value problems with sign-changing Green's function [J].Acta Math Appl Sin Engl Ser,2017,2:263.
[12] Ying W,Jing L,Zengxia C.Positive solutions of periodic boundary value problems for the second-order differential equation with a parameter [J].Bound Value Probl,2017,49:34.
[13] 魏丽萍.一类三阶周期边值共振问题解的存在性 [J].四川大学学报:自然科学版,2018,55:260.
[14] 达举霞,韩晓玲.三阶非线性微分方程边值问题正解的存在性 [J].四川大学学报:自然科学版,2016,53:1177.
[15] 马如云.线性微分方程的非线性扰动 [M].北京:科学出版社,1994.
[16] 郭大均.非线性泛函分析 [M].济南:山东科学技术出版社,1985.引用本文格式:中文:王娇,祝岩.带参数的一阶周期边值问题正解的全局结构 [J].四川大学学报:自然科学版,2019,56:413.英文:Wang J,Zhu Y.Global structure of positive solutions for first-order periodic boundary value problem with parameter [J].J Sichuan Univ:Nat Sci Ed,2019,56:413.
[2] Ruyun M,Lu Z.Construction of lower and upper solutions for first-order periodic problem [J].Bound Value Probl,2015,7:618.
[3] Ruyun M,Jia X.Bifurcation from interval and positive solutions for second-order periodic boundary value problems [J].Dynam Systems Appl,2010,19:211.
[4] Tian J F,Wang W L,Cheng W S.Periodic boundary value problems for first-order impulsive difference equations with time delay [J].Adv Differ Equ,2018,79:2.
[5] Wen G,Shuanghong M,Dabin W.Periodic boundary value problems for first-order difference equations [J].Electron J Qual Theo,2012,52:39.
[6] Wang Z Y,Gao C H.Bifurcation from infinity and multiple solutions for first-order periodic boundary value problems [J].Electron J Differ Equ,2011,141:34.
[7] Ma R Y,Liu Y Q.One-signed periodic solutions of first-order functional differential equations with a parameter [J].Abstr Appl Anal,2011,11:249.
[8] Yuji L.Positive solutions of periodic boundary value problems for nonlinear first-order impulsive differential equations [J].Nonlinear Anal Theor,2009,5:2106.
[9] Tisdell Christopher C.Existence of solutions to first-order periodic boundary value problems [J].J Math Anal Appl,2006,323:1325.
[10] Gurney W S,Blythe S P,Nisbet R N.Nicholson's blowflies revisited [J].Nature,1980,187:17.
[11] Chenghua G,Fei Z,Ruyun M.Existence of positive solutions of second-order periodic boundary value problems with sign-changing Green's function [J].Acta Math Appl Sin Engl Ser,2017,2:263.
[12] Ying W,Jing L,Zengxia C.Positive solutions of periodic boundary value problems for the second-order differential equation with a parameter [J].Bound Value Probl,2017,49:34.
[13] 魏丽萍.一类三阶周期边值共振问题解的存在性 [J].四川大学学报:自然科学版,2018,55:260.
[14] 达举霞,韩晓玲.三阶非线性微分方程边值问题正解的存在性 [J].四川大学学报:自然科学版,2016,53:1177.
[15] 马如云.线性微分方程的非线性扰动 [M].北京:科学出版社,1994.
[16] 郭大均.非线性泛函分析 [M].济南:山东科学技术出版社,1985.引用本文格式:中文:王娇,祝岩.带参数的一阶周期边值问题正解的全局结构 [J].四川大学学报:自然科学版,2019,56:413.英文:Wang J,Zhu Y.Global structure of positive solutions for first-order periodic boundary value problem with parameter [J].J Sichuan Univ:Nat Sci Ed,2019,56:413.