非线性分数阶耦合系统边值问题正解的存在性
发布时间：2018-08-26 09:46
【摘要】：在对分数阶单个系统解的情况的研究基础上,相应的分数阶耦合系统解的存在情况也得到越来越多的关注.本文受此启发,在一类非线性分数阶系统边值问题正解的存在性研究的基础上,进而研究了该边值条件下耦合系统正解的存在情况.所用的主要方法是压缩映射定理,锥上的不动点定理和Schauder不动点定理等定理以及格林函数的相关性质,探讨了分数阶耦合系统在不同条件限制下的正解的存在情况。
[Abstract]:Based on the study of the solution of fractional order single system, more and more attention has been paid to the existence of the corresponding solution of fractional order coupled system. In this paper, based on the study of the existence of positive solutions for a class of nonlinear fractional order boundary value problems, the existence of positive solutions for coupled systems under the boundary value condition is studied. The main methods used are contractive mapping theorem, fixed point theorem and Schauder fixed point theorem on cone, and the related properties of Green's function. The existence of positive solutions of fractional coupled system under different conditions is discussed.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.8
本文编号：2204479
[Abstract]:Based on the study of the solution of fractional order single system, more and more attention has been paid to the existence of the corresponding solution of fractional order coupled system. In this paper, based on the study of the existence of positive solutions for a class of nonlinear fractional order boundary value problems, the existence of positive solutions for coupled systems under the boundary value condition is studied. The main methods used are contractive mapping theorem, fixed point theorem and Schauder fixed point theorem on cone, and the related properties of Green's function. The existence of positive solutions of fractional coupled system under different conditions is discussed.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.8
【参考文献】
相关期刊论文 前1条
1 张萌;孙书荣;赵以阁;杨殿武;;一类分数阶微分方程边值问题正解的存在性[J];济南大学学报(自然科学版);2010年02期
，本文编号：2204479
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