非线性高阶微分与积分耦合系统：有界与无界域上的脉冲与积分方程 Nonlinear Higher Order Differential And Integral Coupled Systems: Impulsive And Integral Equations On Bounded And Unbounded Domains 英文原版 Feliz Manuel Minhós
基本信息
Format Hardback | 244 pages
Dimensions 152.4 x 228.6 x 14.22mm | 494.42g
Publication date 17 May 2022
Publisher World Scientific Publishing Co Pte Ltd
Publication City/Country Singapore, Singapore
Language English
ISBN10 9811225125
ISBN13 9789811225123
书籍信息仅供参考，具体以实物为准
书籍简介
有界或无界区间上的边界值问题，涉及两个或多个具有完全非线性的非线性微分和积分方程的耦合系统，在文献中很少见。作者的这项工作希望能填补这一空白。这里涉及的系统包括有界或无界区间上带有边界约束的Hammerstein型微分和积分方程。这些方程有多种形式和条件（三点式、混合式、函数依赖式、同轴式和异轴式等）。这将是一次系统地研究微分和积分耦合系统。解的存在性，以及在某些情况下，解的定位是在Banach空间进行的，遵循几种类型的论证和方法，如Schauder的定点定理或Guo-Krasnosel的定点定理，与Green的函数或其估计相结合，下解和上解，方便截断，Nagumo条件以不同的形式呈现，等化的概念，Carathéodory函数，以及序列。此外，该卷的后一部分是关于如何将微分耦合系统与积分系统联系起来的一些技术，这需要较少的规则性。在对这项工作进行理论解释的同时，还有一系列涉及真实现象的实际例子和应用，重点是物理学、力学、生物学、林业和动力系统，研究人员和学生会发现这些例子很有用。
Boundary value problems on bounded or unbounded intervals, involving two or more coupled systems of nonlinear differential and integral equations with full nonlinearities, are scarce in the literature. The present work by the authors desires to fill this gap. The systems covered here include differential and integral equations of Hammerstein-type with boundary constraints, on bounded or unbounded intervals. These are presented in several forms and conditions (three points, mixed, with functional dependence, homoclinic and heteroclinic, amongst others). This would be the first time that differential and integral coupled systems are studied systematically. The existence, and in some cases, the localization of the solutions are carried out in Banach space, following several types of arguments and approaches such as Schauder's fixed-point theorem or Guo-Krasnosel'ski? fixed-point theorem in cones, allied to Green's function or its estimates, lower and upper solutions, convenient truncatures, the Nagumo condition presented in different forms, the concept of equiconvergence, Carathéodory functions, and sequences. Moreover, the final part in the volume features some techniques on how to relate differential coupled systems to integral ones, which require less regularity. Parallel to the theoretical explanation of this work, there is a range of practical examples and applications involving real phenomena, focusing on physics, mechanics, biology, forestry, and dynamical systems, which researchers and students will find useful.
作者简介
By (author) Feliz Manuel Minhos , By (author) Robert De Sousa
Feliz Manuel Minhós是数学博士，葡萄牙埃武拉大学数学系教授，数学与应用研究中心（CIMA）协调员，数学博士课程主任，埃武拉大学数学系前主任，许多国际期刊的审稿人、 多份特刊的客座编辑和各种国际期刊的编辑委员会成员，已完成和正在进行的多篇博士论文的导师，各种科学和教学书籍的作者或编辑，以及在国际期刊上发表的约100篇科学论文，涉及数学分析、微分方程、函数分析等不同领域。
Feliz Manuel Minhós is a PhD in Mathematics, Professor in the Department of Mathematics, University of ?vora, Portugal, Coordinator of the Research Centre for Mathematics and Applications (CIMA), Director of the PhD Program in Mathematics and former Head of the Department of Mathematics of the University of ?vora, reviewer of many international journals, Guest Editor of several Special Issues and member of the Editorial Board of various of international journals, Supervisor of several PhD theses concluded and ongoing, author or editor of various scientific and pedagogical books and about hundred scientific papers in international journals, in various fields such as Mathematical Analysis, Differential Equations, Functional analysis, among others.
