Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations by Vicentiu D. Radulescu

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About this book :-
The aim of this book is to present an introduction to a sampling of ideas, phenomena, and methods from the subject of nonlinear elliptic differential equations. One of the main goals of this textbook is to provide the background which is necessary to initiate research work in applied nonlinear analysis. My purpose is to provide for the student a broad perspective in the subject, to illustrate the rich variety of phenomena encompassed by it, and to impart a working knowledge of the most important techniques of analysis of the solutions of the equations. The level of this book is aimed at beginning graduate students. Prerequisites include a truly advanced calculus course, basic knowledge on functional analysis and linear elliptic differential equations, as well as the necessary tools on Sobolev spaces. In this book, we are concerned with some basic monotonicity, analytic, and variational methods which are directly related to the theory of nonlinear partial differential equations of elliptic type. The abstract theorems are applied both to single-valued and to multivalued boundary value problems. This books is develop abstract results in the following three directions: the maximum principle for nonlinear elliptic differential equations, the implicit function theorem, and the critical point theory. In the first category, we are concerned with the method of lower and upper solutions, which is the basic monotonicity principle for proving existence results. The implicit function theorem is used in connection with bifurcation problems, which play a crucial role to explain various phenomena that have been discovered and described in natural sciences over the centuries. The implicit function theorem is one of the oldest paradigms in analysis and is a strong tool in the qualitative analysis of nonlinear problems.

Book Detail :-
This book has following details information.
Title: Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations by Vicentiu D. Radulescu by NA
Publisher: Hindawi Publishing Corporation
Series: FreeCompBooks
Year: 2008
Pages: 210
Type: PDF
Language: English
ISBN-10 #: 9774540395
ISBN-13 #: 978-9774540394
Country: Pakistan
License: N\A
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About Author :-
The author NA NA

Book Contents :-
conver the following topics.
Higher order singular problems - Existence principles for singular problems - Focal problems - (n, p) problem - Conjugate problem - Sturm-Liouville problem - Lidstone problem - Second-order singular problems with f-Laplacian - Dirichlet problem - Periodic problem - Mixed problem - Nonlocal problems - Uniform integrability/equicontinuity - Convergence theorems - Some general existence theorems - Spectrum of the quasilinear Dirichlet problem

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