奇异边值问题组解的存在性和多解性
Existence and Multiplicity Results for Systems of Singular Boundary Value Problems
摘要：
奇异边值问题（SBVPs）出现在数学、工程和物理的各个领域，如边界层理论、气体动力学、核物理、非线性光学等。本专著致力于讨论常微分方程（ODE）的SBVPs系统。它提出了存在性理论的各种问题有无界的非线性区域，他们的解决方案进行了搜索。主要的重点是建立正解的存在性。结果是基于正则化和序贯过程。本论文第一章阐述了研究SBVP的动机。同时也包括了泛函分析和不动点理论的一些有用结果。以下章节包含了作者在巴基斯坦伊斯兰堡国立科技大学的博士论文的结果。这些结果提供了正解的存在性的SBVP具有奇异性的独立和/或因变量以及相对于因变量的第一导数的各种系统。
英文摘要：
Singular boundary value problems (SBVPs) arise in various fields of Mathematics, Engineering and Physics such as boundary layer theory, gas dynamics, nuclear physics, nonlinear optics, etc. The present monograph is devoted to systems of SBVPs for ordinary differential equations (ODEs). It presents existence theory for a variety of problems having unbounded nonlinearities in regions where their solutions are searched for. The main focus is to establish the existence of positive solutions. The results are based on regularization and sequential procedure. First chapter of this monograph describe the motivation for the study of SBVPs. It also include some available results from functional analysis and fixed point theory. The following chapters contain results from author's PhD thesis, National University of Sciences and Technology, Islamabad, Pakistan. These results provide the existence of positive solutions for a variety of systems of SBVPs having singularity with respect to independent and/or dependent variables as well as with respect to the first derivatives of dependent variables.
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