Contributions to Nonlinear Functional Analysis

Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin, Madison, April 12-14, 1971

Eduardo H. Zarantonello

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9780127758503
• eBook ISBN:
  9781483266626
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Contributions to Nonlinear Functional Analysis contains the proceedings of a Symposium on Nonlinear Functional Analysis, held in Madison, Wisconsin, on April 12-14, 1971, under the sponsorship of the University of Wisconsin's Mathematics Research Center. The symposium provided a forum for discussing various topics related to nonlinear functional analysis, from transversality in nonlinear eigenvalue problems to monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations. Comprised of 15 chapters, this book begins by presenting an extension of Leray-Schauder degree and an application to a nonlinear elliptic boundary value problem. The discussion then turns to the use of degree theory to prove the existence of global continua of solutions of nonlinear eigenvalue problems; transversality in nonlinear eigenvalue problems; and how variational structure can be used to study some local questions in bifurcation theory. Subsequent chapters deal with the notion of monotone operators and monotonicity theory; a nonlinear version of the Hille-Yosida theorem; a version of the penalty method for the Navier-Stokes equations; and various types of weak solutions for minimizing problems in the spirit of duality theory for convex functionals. This monograph will be of interest to students and practitioners in the field of mathematics who want to learn more about nonlinear functional analysis.

Table of contents

• Front Cover
• Contributions to Nonlinear Functional Analysis
• Copyright Page
• Table of Contents
• Foreword
• Preface
• Chapter 1. Generalized Degree and Nonlinear Problems
• Chapter 2. A Global Theorem for Nonlinear Eigenvalue Problems and Applications
• Chapter 3. Transversality in Nonlinear Eigenvalue Problems
• Chapter 4. Multiple Eigenvalue Bifurcation for Holomorphic Mappings
• Chapter 5. Monotonicity Methods in Hilbert Spaces and Some Applications to Nonlinear Partial Differential Equations
• Chapter 6. Semigroups of Nonlinear Transformations in Banach Spaces
• Chapter 7. Weak and Strong Solutions of Dual Problems
• Chapter 8. Convex Integral Functionals and Duality
• Chapter 9. Projections on Convex Sets in Hilbert Space and Spectral Theory
• Chapter 10. Nonlinear Functional Analysis and Nonlinear Integral Equations of Hammerstein and Urysohn Type
• Chapter 11. Asymptotic Behaviour of Bounded Solutions of Some Functional Equations
• Chapter 12. Singular Perturbations and Singular Layers in Variational Inequalities
• Chapter 13. Gradient Estimates for Solutions of Nonlinear Elliptic and Parabolic Equations
• Chapter 14. Shock Waves and Entropy
• Chapter 15. The Penalty Method and Some Nonlinear Initial Value Problems
• Index