Boundary Value Problems, Weyl Functions, and Differential Operators
Boundary Value Problems, Weyl Functions, and Differential Operators

Author: Jussi Behrndt

Publisher: Springer Nature

Published: 2020-01-03

Total Pages: 772

ISBN-13: 3030367142

DOWNLOAD EBOOK

This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schrödinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering.

State-Dependent Impulses
State-Dependent Impulses

Author: Irena Rachůnková

Publisher: Springer

Published: 2015-09-29

Total Pages: 194

ISBN-13: 9462391270

DOWNLOAD EBOOK

This book offers the reader a new approach to the solvability of boundary value problems with state-dependent impulses and provides recently obtained existence results for state dependent impulsive problems with general linear boundary conditions. It covers fixed-time impulsive boundary value problems both regular and singular and deals with higher order differential equations or with systems that are subject to general linear boundary conditions. We treat state-dependent impulsive boundary value problems, including a new approach giving effective conditions for the solvability of the Dirichlet problem with one state-dependent impulse condition and we show that the depicted approach can be extended to problems with a finite number of state-dependent impulses. We investigate the Sturm–Liouville boundary value problem for a more general right-hand side of a differential equation. Finally, we offer generalizations to higher order differential equations or differential systems subject to general linear boundary conditions.

Multiple-Scale Analysis of Boundary-Value Problems in Thick Multi-Level Junctions of Type 3:2:2
Multiple-Scale Analysis of Boundary-Value Problems in Thick Multi-Level Junctions of Type 3:2:2

Author: Taras Mel'nyk

Publisher: Springer Nature

Published: 2020-01-03

Total Pages: 111

ISBN-13: 3030355373

DOWNLOAD EBOOK

This book presents asymptotic methods for boundary-value problems (linear and semilinear, elliptic and parabolic) in so-called thick multi-level junctions. These complicated structures appear in a large variety of applications. A concise and readable introduction to the topic, the book provides a full review of the literature as well as a presentation of results of the authors, including the homogenization of boundary-value problems in thick multi-level junctions with non-Lipschitz boundaries, and the construction of approximations for solutions to semilinear problems. Including end-of-chapter conclusions discussing the results and their physical interpretations, this book will be of interest to researchers and graduate students in asymptotic analysis and applied mathematics as well as to physicists, chemists and engineers interested in processes such as heat and mass transfer.

Boundary Value Problems
Boundary Value Problems

Author: Chi Yeung Lo

Publisher: World Scientific

Published: 2000

Total Pages: 282

ISBN-13: 9789810243005

DOWNLOAD EBOOK

This book has been designed for a one-year graduate course on boundary value problems for students of mathematics, engineering, and the physical sciences. It deals mainly with the three fundamental equations of mathematical physics, namely the heat equation, the wave equation, and Laplace's equation. The goal of the book is to obtain a formal solution to a given problem either by the method of separation of variables or by the method of general solutions and to verify that the formal solution possesses all the required properties. To provide the mathematical justification for this approach, the theory of Sturm-Liouville problems, the Fourier series, and the Fourier transform are fully developed. The book assumes a knowledge of advanced calculus and elementary differential equations.

Boundary Value Problems for Elliptic Equations and Systems
Boundary Value Problems for Elliptic Equations and Systems

Author: Guo Chun Wen

Publisher: Chapman & Hall/CRC

Published: 1990

Total Pages: 432

ISBN-13:

DOWNLOAD EBOOK

This monograph mainly deals with several boundary value problems for linear and nonlinear elliptic equations and systems by using function theoretic methods. The established theory is systematic, the considered equations and systems, boundary conditions and domains are rather general. Various methods are used. As an application, the existence of nonlinear quasiconformal mappings onto canonical domains is proved.