Lectures on the Ekeland Variational Principle with Applications and Detours
Author : Djairo Guedes de Figueiredo
Publisher :
Page : 194 pages
File Size : 44,31 MB
Release : 1987
Category :
ISBN :
Author : Djairo Guedes de Figueiredo
Publisher :
Page : 194 pages
File Size : 44,31 MB
Release : 1987
Category :
ISBN :
Author : Djairo G. de Figueiredo
Publisher : Springer
Page : 118 pages
File Size : 29,59 MB
Release : 1989-10-05
Category : Mathematics
ISBN :
Since its publication in 1972, the variational principle of Ekeland has found many applications in different fields of Analysis. Some are very scattered in the literature and therein lies the motivation of these notes. They are intended for the use of students and therefore include several detours through related material. Some readers may be surprised to find a chapter on Nemytskii mappings: however their properties are seldom proved though often referred to and the proofs presented here are more straightforward than those in the standard sources of Krasnoselskii or Vainberg. Two chapters cover applications to (semilinear elliptic) PDE. The central chapter is on Brézis' proof of the minimax theorems of Ambrosetti and Rabinowitz. To keep the text self-contained, some convex analysis is developed (for the treatment of the duality mapping) and some geometry of Banach spaces. These notes are based on a course given by the author at the Tata Institute in 1987.
Author : D. G. De Figueiredo
Publisher :
Page : 96 pages
File Size : 46,80 MB
Release : 1989
Category :
ISBN :
Author : Diairo Guedes de Figueiredo
Publisher :
Page : 96 pages
File Size : 31,75 MB
Release : 1989
Category :
ISBN : 9788185198194
Author : Irina Meghea
Publisher : Archives contemporaines
Page : 535 pages
File Size : 41,6 MB
Release : 2009
Category : Banach spaces
ISBN : 2914610963
Author : Dumitru Motreanu
Publisher : Springer Science & Business Media
Page : 465 pages
File Size : 41,89 MB
Release : 2013-11-19
Category : Mathematics
ISBN : 1461493234
This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study. The authors first give a comprehensive introduction to the many different classical methods from nonlinear analysis, variational principles, and Morse theory. They then provide a rigorous and detailed treatment of the relevant areas of nonlinear analysis with new applications to nonlinear boundary value problems for both ordinary and partial differential equations. Recent results on the existence and multiplicity of critical points for both smooth and nonsmooth functional, developments on the degree theory of monotone type operators, nonlinear maximum and comparison principles for p-Laplacian type operators, and new developments on nonlinear Neumann problems involving non-homogeneous differential operators appear for the first time in book form. The presentation is systematic, and an extensive bibliography and a remarks section at the end of each chapter highlight the text. This work will serve as an invaluable reference for researchers working in nonlinear analysis and partial differential equations as well as a useful tool for all those interested in the topics presented.
Author : Qamrul Hasan Ansari
Publisher : Cambridge University Press
Page : 234 pages
File Size : 39,20 MB
Release : 2023-08-31
Category : Mathematics
ISBN : 1009351451
A book covering theory and examples for undergraduates, graduates, and researchers studying fixed point theory or nonlinear analysis.
Author : Zdzislaw Denkowski
Publisher : Springer Science & Business Media
Page : 844 pages
File Size : 47,80 MB
Release : 2003-01-31
Category : Computers
ISBN : 9780306474569
This book offers an exposition of the main applications of Nonlinear Analysis, beginning with a chapter on Nonlinear Operators and Fixed Points, a connecting point and bridge from Nonlinear Analysis theory to its applications. The topics covered include applications to ordinary and partial differential equations, optimization, optimal control, calculus of variations and mathematical economics. The presentation is supplemented with the inclusion of many exercises and their solutions.
Author : A. S. GUPTA
Publisher : PHI Learning Pvt. Ltd.
Page : 256 pages
File Size : 36,22 MB
Release : 1996-01-01
Category : Mathematics
ISBN : 8120311205
Calculus of variations is one of the most important mathematical tools of great scientific significance used by scientistis and engineers. Unfortunately, a few books that are available are written at a level which is not easily comprehensible for postgraduate students.This book, written by a highly respected academic, presents the materials in a lucid manner so as to be within the easy grasp of the students with some background in calculus, differential equations and functional analysis. The aim is to give a thorough and systematic analysis of various aspects of calculus of variations.
Author : Youssef Jabri
Publisher : Cambridge University Press
Page : 390 pages
File Size : 45,21 MB
Release : 2003-09-15
Category : Mathematics
ISBN : 9781139440813
This 2003 book presents min-max methods through a study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led from the most accessible results to the forefront of the theory, and at each step in this walk between the hills, the author presents the extensions and variants of the MPT in a complete and unified way. Coverage includes standard topics, but it also covers other topics covered nowhere else in book form: the non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants. Each chapter has a section with supplementary comments and bibliographical notes, and there is a rich bibliography and a detailed index to aid the reader. The book is suitable for researchers and graduate students. Nevertheless, the style and the choice of the material make it accessible to all newcomers to the field.