Methods in Nonlinear Integral Equations

ISBN-13: 9781402008443 / Angielski / Twarda / 2002 / 218 str.

Radu Precup; R. Precup

Opis

Methods in Nonlinear Integral Equations presents several extremely fruitful methods for the analysis of systems and nonlinear integral equations. They include: fixed point methods (the Schauder and Leray-Schauder principles), variational methods (direct variational methods and mountain pass theorems), and iterative methods (the discrete continuation principle, upper and lower solutions techniques, Newton's method and the generalized quasilinearization method). Many important applications for several classes of integral equations and, in particular, for initial and boundary value problems, are presented to complement the theory. Special attention is paid to the existence and localization of solutions in bounded domains such as balls and order intervals. The presentation is essentially self-contained and leads the reader from classical concepts to current ideas and methods of nonlinear analysis.
This work will be of interest to graduate students and theoretical and applied mathematicians in nonlinear functional analysis, integral equations, ordinary and partial differential equations, and related fields.

Recenzje

From the reviews:

"This book deals with several methods of nonlinear analysis for the investigation of nonlinear integral equations ... . Necessary abstract results of nonlinear analysis ... are provided. ... new points of view, extensions and applications are presented. ... The presentation is self-contained and therefore should be useful to find the current ideas and methods." (V. Lakshmikantham, Zentralblatt MATH, Vol. 1060 (11), 2005)

Spis treści

Preface. Notation. Overview. I: Fixed Point Methods. 1. Compactness in Metric Spaces. 2. Completely Continuous Operators on Banach Spaces. 3. Continuous Solutions of Integral Equations via Schauder's Theorem. 4. The Leray-Schauder Principle and Applications. 5. Existence Theory in LP Spaces. References: Part I. II: Variational Methods. 6. Positive Self-Adjoint Operators in Hilbert Spaces. 7. The Fréchet Derivative and Critical Points of Extremum. 8. The Mountain Pass Theorem and Critical Points of Saddle Type. 9. Nontrivial Solutions of Abstract Hammerstein Equations. References Part II. III: Iterative Methods. 10. The Discrete Continuation Principle. 11. Monotone Iterative Methods. 12. Quadratically Convergent Methods. References: Part III. Index.