This book describes many new results and extensions of the theory of generalized topological degree for densely defined A-proper operators and presents important applications, particularly to boundary value problems of nonlinear ordinary and partial differential equations that are intractable under any other existing theory. A-proper mappings arise naturally in the solution to an equation in infinite dimensional space via the finite dimensional approximation. The theory subsumes classical theory involving compact vector fields as well as the more recent theories of condensing vector-fields, strongly monotone, and strongly accretive maps. Researchers and graduate students in mathematics, applied mathematics, and physics who make use of nonlinear analysis will find this an important resource for new techniques.
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'The book presents new and well-known results in a unified approach.' European Mathematical Society Newsletter
Book Description
This book describes many new results and extensions of the theory of generalized topological degree for densely defined A-proper operators, which arise in the solution of infinite dimensional equations via the finite dimensional approximation. The author presents important applications to boundary value problems of nonlinear ordinary and partial differential equations which are intractable under any other existing theory. Researchers and graduate students in mathematics, applied mathematics, and physics who make use of nonlinear analysis will find this an important resource.
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Inside This Book
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First Sentence:
Let X and Y be real separable Banach spaces, D a subset of X, T: D X Y a possibly nonlinear mapping, and 0 = {Xn, Pn; Yn, Qn} a suitable approximation scheme for the equation (I) T(x) = y, x D, y Y. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
variational solvability, projectionally complete scheme, constructive solvability, compact vector fields, global bifurcation results, admissible scheme, coincidence degree theory, semilinear abstract, generalized topological degree, fixed point index, nonlinear elliptic boundary value problems, semilinear equations, solvability results, generalized degree, imbedding theorem, covering dimension, accretive operators, continuous bilinear form, mapping theory, compact maps, nonlinear elliptic equations, partial inverse, bifurcation theorem, nonlinear boundary value problems, projection scheme Key Phrases - Capitalized Phrases (CAPs): (learn more)
Improved Solvability Results, Notes Section, New Approach New!
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Let X and Y be real separable Banach spaces, D a subset of X, T: D X Y a possibly nonlinear mapping, and 0 = {Xn, Pn; Yn, Qn} a suitable approximation scheme for the equation (I) T(x) = y, x D, y Y. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
variational solvability, projectionally complete scheme, constructive solvability, compact vector fields, global bifurcation results, admissible scheme, coincidence degree theory, semilinear abstract, generalized topological degree, fixed point index, nonlinear elliptic boundary value problems, semilinear equations, solvability results, generalized degree, imbedding theorem, covering dimension, accretive operators, continuous bilinear form, mapping theory, compact maps, nonlinear elliptic equations, partial inverse, bifurcation theorem, nonlinear boundary value problems, projection scheme Key Phrases - Capitalized Phrases (CAPs): (learn more)
Improved Solvability Results, Notes Section, New Approach New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Citations (learn more)
This book cites 18
books:
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2
books
cite this book:
- Sobolev spaces, Volume 65 (Pure and Applied Mathematics) by Author Unknown in Back Matter (1), Back Matter (2), and Back Matter (3)
- Measure and Integral: An Introduction to Real Analysis (Chapman & Hall/CRC Pure and Applied Mathematics) by Richard Wheeden in Back Matter (1), and Back Matter (2)
- Perturbation Theory for Linear Operators (Classics in Mathematics) by Tosio Kato in Back Matter
- Functional Analysis (Springer Classics in Mathematics) by Kosaku Yosida in Back Matter
- Nonlinear Functional Analysis and Differential Equations (Lecture Notes in Pure and Applied Mathematics) by Cesari in Back Matter
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