删除或更新信息,请邮件至freekaoyan#163.com(#换成@)

具有非局部Stieltjes积分边值条件半正(k,n-k)边值问题的非平凡解

本站小编 Free考研考试/2021-12-27

具有非局部Stieltjes积分边值条件半正(k,n-k)边值问题的非平凡解 尹晨阳, 马跃萧, 张国伟东北大学数学系, 沈阳 110819 Nontrivial Solutions of Semi-positone (k, n-k) Boundary Value Problem Subject to Nonlocal Boundary Conditions with Stieltjes Integrals YIN Chenyang, MA Yuexiao, ZHANG GuoweiDepartment of Mathematics, Northeastern University, Shenyang 110819, China
摘要
图/表
参考文献
相关文章(15)
点击分布统计
下载分布统计
-->

全文: PDF(361 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)
摘要应用拓扑度方法证明了具有非局部Stieltjes积分边值条件半正(k,n-k)边值问题非平凡解的存在性,其中非线性项f可以不是非负的但下方有界.给出了正解存在性的两个推论,它们是非线性项f非负情形已有结论的推广.通过两个例子来说明主要结论,例子的混合边值条件包含变号系数的多点条件和变号核的积分条件.
服务
加入引用管理器
E-mail Alert
RSS
收稿日期: 2018-09-25
PACS:O175.14
O177.91
基金资助:国家自然科学基金(61473065),国家级大学生创新创业训练计划(201810145026)资助项目.

引用本文:
尹晨阳, 马跃萧, 张国伟. 具有非局部Stieltjes积分边值条件半正(k,n-k)边值问题的非平凡解[J]. 应用数学学报, 2020, 43(1): 62-78. YIN Chenyang, MA Yuexiao, ZHANG Guowei. Nontrivial Solutions of Semi-positone (k, n-k) Boundary Value Problem Subject to Nonlocal Boundary Conditions with Stieltjes Integrals. Acta Mathematicae Applicatae Sinica, 2020, 43(1): 62-78.
链接本文:
http://123.57.41.99/jweb_yysxxb/CN/ http://123.57.41.99/jweb_yysxxb/CN/Y2020/V43/I1/62


[1] Webb J R L, Infante G. Non-local boundary value problems of arbitrary order. J. London Math. Soc., 2009, 79(1):238-259
[2] Webb J R L, Infante G. Positive solutions of nonlocal boundary value problems:a unified approach. J. London Math. Soc., 2006, 74(2):673-693
[3] Webb J R L. Nonlocal conjugate type boundary value problems of higher order. Nonlinear Anal., 2009, 71(5-6):1933-1940
[4] Webb J R L. Positive solutions of some higher order nonlocal boundary value problems. Electron J. Qual. Theory Differ. Equ., 2009, 29:1-15
[5] Hao X, Liu L, Wu Y, et al. Positive solutions for nonlinear nth-order singular eigenvalue problem with nonlocal conditions. Nonlinear Anal., 2010, 73(6):1653-1662
[6] Lan K Q. Multiple positive solutions of conjugate boundary value problems with singularities. Appl. Math. Comput., 2004, 147(2):461-474
[7] Lan K Q. Multiple positive eigenvalues of conjugate boundary value problems with singularities. Discrete Contin. Dyn. Syst., 2003, suppl:501-506
[8] Su H, Wang X. Positive solutions to singular semipositone m-point n-order boundary value problems. J. Appl. Math. Comput., 2011, 36(1):187-200
[9] Su H, Wei Z. Positive solutions to semipositone (k, n-k) conjugate eigenvalue problems. Nonlinear Anal., 2008, 69(9):3190-3201
[10] Zhang M, Yin Y, Wei Z. Existence of positive solution for singular semi-positone (k, n-k) conjugate m-point boundary value problem. Comput. Math. Appl., 2008, 56(4):1146-1154
[11] Webb J R L, Infante G. Semi-positone nonlocal boundary value problems of arbitrary order. Commun. Pure Appl. Anal., 2010, 9(2):563-581
[12] Cui Y, Zou Y. Monotone iterative technique for (k, n-k) conjugate boundary value problems. Electron J. Qual. Theory Differ. Equ., 2015, 69:1-11
[13] Lin X, Jiang D, Li X. Existence and uniqueness of solutions for singular (k, n-k) conjugate boundary value problems. Comput. Math. Appl., 2006, 52(3-4):375-382
[14] Sun J, Zhang G. Nontrivial solutions of singular sublinear Sturm-Liouville problems. J. Math. Anal. Appl., 2007, 326(1):242-251
[15] Sun J, Zhang G. Nontrivial solutions of singular superlinear Sturm-Liouville problems. J. Math. Anal. Appl., 2006, 313(2):518-536
[16] Yang B. Upper estimate for positive solutions of the (p,n-p) conjugate boundary value problem. J. Math. Anal. Appl., 2012, 390(2):535-548
[17] Yang B. Positive solutions of the (n-1, 1) conjugate boundary value problem. Electron J. Qual. Theory Differ. Equ., 2010, 53:1-13
[18] Zhang G, Sun J. Positive solutions of m-point boundary value problems. J. Math. Anal. Appl., 2004, 291(2):406-418
[19] 张国伟, 孙经先. 奇异(k, n-k)多点边值问题的正解. 数学学报, 2006, 49(2):391-398(Zhang G, Sun J. Positive solutions of singular (k, n-k) multi-point boundary value problems. Acta Math. Sinica), 2006, 49(2):391-398)
[20] Deimling K. Nonlinear Functional Analysis. Berlin:Springer-Verlag, 1985
[21] 郭大钧. 非线性泛函分析(第三版). 北京:高等教育出版社, 2015(Guo D. Nonlinear Functional Analysis (third edition). Beijing:Higher Education Press, 2015)
[22] 张国伟. 不动点方法的理论及应用. 北京:科学出版社, 2017(Zhang G. The theory and Applications of Fixed Point Methods. Beijing:Science Press, 2017)
[23] 蒋达清. 奇异(k,n-k)共轭边值问题的正解. 数学学报, 2001, 44(3):541-548(Jiang D. Positive Solutions to Singular (k,n-k) Conjugate Boundary Value Problems. Acta Math. Sinica, 2001, 44(3):541-548)
[24] Kong L, Wang J. The Green's function for (k,n-k) conjugate boundary value problems and its applications. J. Math. Anal. Appl., 2001, 255(2):404-422
[25] 孙经先. 非线性泛函分析及其应用. 北京:高等教育出版社, 2007(Sun J. Nonlinear Functional Analysis and Its Applications. Beijing:Science Press, 2007)
[26] Berezin I S, Zhidkov N P. Computing Methods (Vol I). Oxford:Pergamon Press, 1965
[27] Martin R H. Nonlinear Operators and Differential Equations in Banach Spaces. New York:Wiley, 1976
[28] Webb J R L, Lan K Q. Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary value problems of local and nonlocal type. Topol. Methods Nonlinear Anal., 2006, 27(1):91-115
[29] Cui Y, Zou Y. Nontrivial solutions of singular superlinear m-point boundary value problems. Appl. Math. Comput., 2007, 187(2):1256-1264

[1]冯立杰. 具有分数阶导数的积分边值问题正解的存在性[J]. 应用数学学报, 2019, 42(2): 254-265.
[2]陈瑞鹏, 李小亚. 一类核反应堆数学模型正解的全局分歧[J]. 应用数学学报, 2018, 41(5): 596-608.
[3]田元生, 李小平, 葛渭高. p-Laplacian分数阶微分方程边值问题正解的存在性[J]. 应用数学学报, 2018, 41(4): 529-539.
[4]李圆晓, 高文杰. 具变号权函数的拟线性椭圆方程组多重解的存在性[J]. 应用数学学报, 2018, 41(1): 71-82.
[5]王亚平, 刘立山, 吴永洪. 有Riemann-Stieltjes积分边界条件的非线性奇异分数阶微分方程边值问题正解的存在性[J]. 应用数学学报, 2017, 40(5): 752-769.
[6]胡良根, 张怀念. 奇异Sturm-Liouville特征值问题正解的全局分歧和存在性[J]. 应用数学学报, 2016, 39(5): 677-688.
[7]田元生, 李小平. 一类带p-Laplacian算子分数阶微分方程边值问题的正解[J]. 应用数学学报, 2016, 39(4): 481-494.
[8]廖芳芳, 唐先华, 张健. IRN上周期Hamilton型椭圆系统新的超线性条件[J]. 应用数学学报, 2015, 38(6): 987-1000.
[9]王金华, 向红军. 无穷分数差分方程三点边值问题[J]. 应用数学学报, 2015, 38(6): 1029-1039.
[10]樊自安. 包含次临界和临界Sobolev指数的椭圆方程组解的存在性[J]. 应用数学学报, 2015, 38(5): 834-844.
[11]张立新. 一类含积分边界条件的分数阶微分方程的正解的存在性[J]. 应用数学学报, 2015, 38(3): 423-433.
[12]梁海华, 王根强. 一类带非负系数矩阵的非线性代数系统的正解的存在性[J]. 应用数学学报, 2015, 38(1): 137-149.
[13]王峰, 崔玉军. 二阶隐式微分方程周期边值问题的正解[J]. 应用数学学报(英文版), 2014, 37(5): 946-955.
[14]汪继秀. 一类带非线性边值条件的半线性椭圆方程组的多个解[J]. 应用数学学报(英文版), 2014, 37(2): 332-342.
[15]赵昕, 常小军. 一类分数阶椭圆型方程解的多重性[J]. 应用数学学报(英文版), 2014, 37(1): 138-144.



PDF全文下载地址:

http://123.57.41.99/jweb_yysxxb/CN/article/downloadArticleFile.do?attachType=PDF&id=14711
相关话题/应用数学 分数 北京 数学 统计