超前型无穷奇异二阶Neumann边值问题的无穷正解
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摘要
为了研究一类具有超前型偏差变元以及无穷多个奇异点的二阶Neumann微分方程边值问题无穷多个正解的存在性,利用Banach空间中范数形式的锥拉伸与压缩不动点定理给出了存在无穷多个正解的一些新的充分条件。最后,通过一个例子验证了定理的条件是合理的。
To investigate the existence of multiple positive solutions for Neumann boundary value problems of second-order differential equations with infinitely many singularities and advanced deviating argument,we establish the new sufficient conditions for the existence of three positive solutions by using fixed point theorem of the cone expansion and compression of norm type in Banach space. Finally,an example is included to illustrate the rationality of the conditions in the main result.
To investigate the existence of multiple positive solutions for Neumann boundary value problems of second-order differential equations with infinitely many singularities and advanced deviating argument,we establish the new sufficient conditions for the existence of three positive solutions by using fixed point theorem of the cone expansion and compression of norm type in Banach space. Finally,an example is included to illustrate the rationality of the conditions in the main result.
引文
[1]卢高丽,冯美强。具偏差变元的二阶微分方程多个正解及其应用[J].中国科技论文,2016,11(5):571-575.
[2]Jiang Daqing,Liu Huizhao.Existence of positive solutions to second order singular Neumann boundary value problems[J].Journal of Mathematical research and exposition,2010,20(3):360-364.
[3]Sun Yan,Cho Yeol Je,Donal O’Regan.Positive solutions for singular second order Neumann boundary value problems via a cone fixed point theorem[J].Appl Math Comput,2009,210(1):80-86.
[4]张兴秋,孙永平,仲秋艳.奇异二阶Neumann边值问题的正解[J].工程数学学报,2004,21(4):645-648.
[5]马如云,陈瑞鹏,李杰梅.非线性Neumann问题正解的存在性[J].数学学报,2013,56(3):289-300.
[6]梁盛泉.二阶Neumann边值问题的正解[J].甘肃农业大学学报,2007,42(3):122-125.
[7]Liu Xiaoya,Li Yongxiang.Positive solutions for Neumann boundary value problems of secondorder impulsive differential equations in Banach spaces[J].Abstr Appl Anal,2012(1):1-18.
[8]Eric R Kaufmann,Nickolai Kosmatov.A multiplicity result for a boundary value problem with infinitely many singularities[J].J Math Anal Appl,2002,269(2):444-453.
[9]郭大钧.非线性泛函分析[M].北京:高等教育出版社,2015:243-245.
[10]Sun Jianping,Li Wantong.Multiple positive solutions to second-order Neumann boundary value problems[J].Appl Math Comput,2003,146(1):187-194.
[11]Xing Hui,Chen Hongbin,He Xibin.Exact multiplicity and stability of solutions of secondorder Neumann boundary value problem[J].Appl Math Comput,2014,232(3):1104-1111.
[12]Zhang Xuemei,Feng Meiqiiang.Positive solutions for a second-order differential equation with integral boundary conditions and deviating arguments[J].Boundary Value Problems,2015,222(1):1-21.
[2]Jiang Daqing,Liu Huizhao.Existence of positive solutions to second order singular Neumann boundary value problems[J].Journal of Mathematical research and exposition,2010,20(3):360-364.
[3]Sun Yan,Cho Yeol Je,Donal O’Regan.Positive solutions for singular second order Neumann boundary value problems via a cone fixed point theorem[J].Appl Math Comput,2009,210(1):80-86.
[4]张兴秋,孙永平,仲秋艳.奇异二阶Neumann边值问题的正解[J].工程数学学报,2004,21(4):645-648.
[5]马如云,陈瑞鹏,李杰梅.非线性Neumann问题正解的存在性[J].数学学报,2013,56(3):289-300.
[6]梁盛泉.二阶Neumann边值问题的正解[J].甘肃农业大学学报,2007,42(3):122-125.
[7]Liu Xiaoya,Li Yongxiang.Positive solutions for Neumann boundary value problems of secondorder impulsive differential equations in Banach spaces[J].Abstr Appl Anal,2012(1):1-18.
[8]Eric R Kaufmann,Nickolai Kosmatov.A multiplicity result for a boundary value problem with infinitely many singularities[J].J Math Anal Appl,2002,269(2):444-453.
[9]郭大钧.非线性泛函分析[M].北京:高等教育出版社,2015:243-245.
[10]Sun Jianping,Li Wantong.Multiple positive solutions to second-order Neumann boundary value problems[J].Appl Math Comput,2003,146(1):187-194.
[11]Xing Hui,Chen Hongbin,He Xibin.Exact multiplicity and stability of solutions of secondorder Neumann boundary value problem[J].Appl Math Comput,2014,232(3):1104-1111.
[12]Zhang Xuemei,Feng Meiqiiang.Positive solutions for a second-order differential equation with integral boundary conditions and deviating arguments[J].Boundary Value Problems,2015,222(1):1-21.