几类非线性积分微分方程解的存在性和唯一性
发布时间：2018-11-09 12:27
【摘要】：本文共分为二章.第一章主要研究Banach空间中带有Riemann-Stieltjes型积分条件的非线性分数阶积分微分方程的解的存在性和唯一性.通过Green函数的性质、Holder不等式、Banach压缩映射原理、Schauder不动点定理得到了解的存在性和唯一性结果.第二章主要研究一类带有Riemann-Stieltjes型积分边值条件的非线性分数阶微分方程解的存在性问题,本文通过利用相关Green函数的不等式以及锥拉伸压缩不动点定理得到正解的存在性.我们推广和改进了包括奇异及非奇异两种情况的一些已知结果.
[Abstract]:This paper is divided into two chapters. In chapter 1, we study the existence and uniqueness of solutions for nonlinear fractional integrodifferential equations with Riemann-Stieltjes type integral conditions in Banach spaces. The existence and uniqueness of the solution are obtained by the properties of Green function, Holder inequality, Banach contraction mapping principle and Schauder fixed point theorem. In the second chapter, we study the existence of solutions for a class of nonlinear fractional differential equations with Riemann-Stieltjes type integral boundary value conditions. In this paper, we obtain the existence of positive solutions by using the inequality of Green function and the fixed point theorem of cone stretching contraction. We generalize and improve some known results including singular and nonsingular cases.
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.6
本文编号：2320411
[Abstract]:This paper is divided into two chapters. In chapter 1, we study the existence and uniqueness of solutions for nonlinear fractional integrodifferential equations with Riemann-Stieltjes type integral conditions in Banach spaces. The existence and uniqueness of the solution are obtained by the properties of Green function, Holder inequality, Banach contraction mapping principle and Schauder fixed point theorem. In the second chapter, we study the existence of solutions for a class of nonlinear fractional differential equations with Riemann-Stieltjes type integral boundary value conditions. In this paper, we obtain the existence of positive solutions by using the inequality of Green function and the fixed point theorem of cone stretching contraction. We generalize and improve some known results including singular and nonsingular cases.
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.6
【参考文献】
相关期刊论文 前1条
1 Dimplekumar;N. CHALISHAJAR;K. KARTHIKEYAN;;EXISTENCE AND UNIQUENESS RESULTS FOR BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS INVOLVING GRONWALL'S INEQUALITY IN BANACH SPACES[J];Acta Mathematica Scientia;2013年03期
，本文编号：2320411
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