topological methods in the study of boundary value problems

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Topological Methods In The Study Of Boundary Value Problems

Author : Pablo Amster
ISBN : 9781461488934
Genre : Mathematics
File Size : 61. 95 MB
Format : PDF
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This textbook is devoted to the study of some simple but representative nonlinear boundary value problems by topological methods. The approach is elementary, with only a few model ordinary differential equations and applications, chosen in such a way that the student may avoid most of the technical difficulties and focus on the application of topological methods. Only basic knowledge of general analysis is needed, making the book understandable to non-specialists. The main topics in the study of boundary value problems are present in this text, so readers with some experience in functional analysis or differential equations may also find some elements that complement and enrich their tools for solving nonlinear problems. In comparison with other texts in the field, this one has the advantage of a concise and informal style, thus allowing graduate and undergraduate students to enjoy some of the beauties of this interesting branch of mathematics. Exercises and examples are included throughout the book, providing motivation for the reader.

Topological Methods For Asymmetric Boundary Value Problems

Author : Patrick J. McKenna
ISBN : UOM:39015037459909
Genre : Boundary value problems
File Size : 70. 63 MB
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Methods For Analysis Of Nonlinear Elliptic Boundary Value Problems

Author : I. V. Skrypnik
ISBN : 082189756X
Genre : Mathematics
File Size : 25. 29 MB
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The theory of nonlinear elliptic equations is currently one of the most actively developing branches of the theory of partial differential equations. This book investigates boundary value problems for nonlinear elliptic equations of arbitrary order. In addition to monotone operator methods, a broad range of applications of topological methods to nonlinear differential equations is presented: solvability, estimation of the number of solutions, and the branching of solutions of nonlinear equations. Skrypnik establishes, by various procedures, a priori estimates and the regularity of solutions of nonlinear elliptic equations of arbitrary order. Also covered are methods of homogenization of nonlinear elliptic problems in perforated domains. The book is suitable for use in graduate courses in differential equations and nonlinear functional analysis.

Variational And Topological Methods In The Study Of Nonlinear Phenomena

Author : V. Benci
ISBN : 0817642781
Genre : Mathematics
File Size : 62. 1 MB
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Topological And Variational Methods With Applications To Nonlinear Boundary Value Problems

Author : Dumitru Motreanu
ISBN : 9781461493235
Genre : Mathematics
File Size : 75. 16 MB
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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.

Topological Methods In Nonlinear Analysis

Author :
ISBN : UOM:39015072629846
Genre : Topology
File Size : 44. 42 MB
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An Introduction To Nonlinear Boundary Value Problems

Author : Lakshmikantham
ISBN : 9780080956183
Genre : Computers
File Size : 71. 15 MB
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A book on an advanced level that exposes the reader to the fascinating field of differential equations and provides a ready access to an up-to-date state of this art is of immense value. This book presents a variety of techniques that are employed in the theory of nonlinear boundary value problems. For example, the following are discussed: methods that involve differential inequalities; shooting and angular function techniques; functional analytic approaches; topological methods.

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