【作者】 赵以安；

【导师】 宋光兴；

【作者基本信息】 中国石油大学 ， 数学， 2010， 硕士

【摘要】 非线性泛函分析是现代分析数学的一个重要分支,它能够清楚地解释自然界中很多自然现象,因而受到了越来越多的数学家与数学工作者的关注.其中,非线性问题来源于应用数学和物理的多个分支,是目前分析数学中研究最为活跃的领域之一.本论文主要讨论了带有casual算子的一阶混合型脉冲积-微分方程积分边值问题,混合型脉冲积分-微分方程积分边值问题,混合型脉冲积-微分方程的非线性边值问题解的存在性,全文共分四章.第一章,前言部分,主要介绍了选题来源、研究意义、国内外研究现状,以及论文的主要研究内容和目标.第二章,利用新的比较原理和上下解方法,讨论了具有casual算子的一阶混合型脉冲方程积分边值问题,并改进了某些已有的结果.第三章,利用单调迭代方法,研究了一阶混合型脉冲积分-微分方程积分边值问题极值解和唯一解的存在性.第四章,利用上下解方法,研究了一阶混合型脉冲积-微分方程的非线性边值问题唯一解的存在性,对某些已有结果作了推广和改进.更多还原

【Abstract】 Nonlinear functional analysis is an important branch of modern analysis mathematics. It can explain a lot of natural phenomena clearly, so more and more mathematical researchers are devoting their time to it. Among them, the nonlinear problem comes from a lot of branches of applied mathematics and physics, it is at present one of the most active fields that is studied in analysical mathematics.The present thesis mainly discusses the problems for solutions of integral boundary value problems with causal operators , integral boundary value problems for first order impulsive integro-differential equations of mixed type and nonlinear boundary value problems for first order impulsive integro-differential equations of mixed type.In chapter one, we mainly introduce background, research meaning and current situations of this study, and the main conclusions and motive of this thesis.In chapter two, we discuss the existence of solutions of f integral boundary value problems with causal operators, by using a comparison result and partial method. It generalizes and improves some former corresponding results.In chapter three, by using the cone theory and monotone iterative technique, we investigate the existence of extremal solutions and unique solutions of integral boundary value problems for first order impulsive integro-differential equations of mixed type. Our results improve and extend many recent results.In chapter four, by using lower and upper solutions, we investigate the existence of unique solution of nonlinear boundary value problems for first order impulsive integro-differential equations of mixed type. Our results improve and extend some recent results.更多还原