高阶微分方程边值问题3个正解的存在性
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摘要
主要讨论了一类高阶两点边值问题,首先利用已知的高阶两点边值问题的格林函数得到相关性质的结果,其次再利用Leggett-Williams不动点定理,详细研究以下高阶两点边值问题■3个正解的存在性,其中n≥2,p∈{1,2,…,n-2}.
A class of high order two-point boundary value problems has been discussed. Firstly using the green's function of the higher order two-point boundary value problem, the related properties have been obtained. Using the Leggett-Williams Fixed-Point Theorem, the existence of multiple solutions of following high order boundary value problem has been studied ■ where n≥2, p∈{1, 2, …, n-2}.
A class of high order two-point boundary value problems has been discussed. Firstly using the green's function of the higher order two-point boundary value problem, the related properties have been obtained. Using the Leggett-Williams Fixed-Point Theorem, the existence of multiple solutions of following high order boundary value problem has been studied ■ where n≥2, p∈{1, 2, …, n-2}.
引文
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[5] 唐榆婷,唐春雷.一类带Hardy-Sobolev临界指数的Kirchhoff方程正解的存在性 [J].西南大学学报(自然科学版),2017,39(6):81-86.
[6] 贾秀玲,段誉.一类带线性项非局部问题解的存在性与非存在性 [J].西南师范大学学报(自然科学版),2018,43(10):22-25.
[7] LEGGETT R W,WILLIANS L R.Multiple Positive Fixed Solutions of Nonlinear Operarors on Ordered Banach Spaces [J].Indiana Univ Math J,1979,28:673-677.
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[11] DONG S J,GE W G,Positive Solutions of an m-Point Boundary Value Problem with Sign Changing Nonlinearities [J].Comput Math Appl,2005,49(4):589-598.
[12] 葛渭高.非线性常微分方程边值问题 [M].北京:科学出版社,2007.
[2] 徐登洲,马如云.线性微分方程的非线性扰动 [M].2版.北京:科学出版社,2008.
[3] 马如云.非线性常微分方程非局部问题 [M].北京:科学出版社,2004.
[4] 黄链,邓磊.C*-代数值b-度量空间中不动点的存在性与唯一性 [J].西南大学学报(自然科学版),2017,39(2):55-59.
[5] 唐榆婷,唐春雷.一类带Hardy-Sobolev临界指数的Kirchhoff方程正解的存在性 [J].西南大学学报(自然科学版),2017,39(6):81-86.
[6] 贾秀玲,段誉.一类带线性项非局部问题解的存在性与非存在性 [J].西南师范大学学报(自然科学版),2018,43(10):22-25.
[7] LEGGETT R W,WILLIANS L R.Multiple Positive Fixed Solutions of Nonlinear Operarors on Ordered Banach Spaces [J].Indiana Univ Math J,1979,28:673-677.
[8] AVERY R I,HENDERSON J.Three Symmetric Positive Solutons for a Second Order Boundary Value Problem [J].Appl Math Lett,2000,13:1-7.
[9] AVERY R I,PETERSON A C.Three Positive Fixed Points of Nonlinear Operators on Ordered Banach Spaces [J].Comput Math Appl,2001,42:313-322.
[10] ANDERSON D,AVERY R I.Multiple Positive Solutions to a Third-Order Discrete Focal Boundary Value Problem [J].Comput Math Appl,2001,41(3-5):333-340.
[11] DONG S J,GE W G,Positive Solutions of an m-Point Boundary Value Problem with Sign Changing Nonlinearities [J].Comput Math Appl,2005,49(4):589-598.
[12] 葛渭高.非线性常微分方程边值问题 [M].北京:科学出版社,2007.