Fundamentals of Applied Functional Analysis (Monographs and Surveys in Pure and Applied Mathematics 91)

Fundamentals of Applied Functional Analysis (Monographs and Surveys in Pure and Applied Mathematics 91)

By: Dragisa Mitrovic (author), Darko Zubrinic (author)Hardback

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Description

This volume provides an introduction to modern concepts of linear and nonlinear functional analysis. It may serve as a preparation for study of the abundant scientific literature on the theory of distributions, Sobolev spaces, elliptic equations and nonlinear analysis. Its purpose is also to provide an insight into the variety of deeply interlaced mathematical tools applied in the study of nonlinear problems. It starts with a review of the basics of Lebesgue spaces and Nemytzki operators. Special attention is paid to distributions, Sobelev spaces and their applications to the study of elliptic boundary value problems. Some of the methods of nonlinear analysis are illustrated by: resonant and nonresonant problems; lower semicontinuity and convexity; energy functionals; monotone operators; reduction method; Landesman-Lazer problems; jumping nonlinearities; the Mountain-Pass theorem; and topological degree. The book contains numerous examples and exercises, most with detailed solutions and hints.

Contents

Lebesgue Measure. Lebesgue Integral. Lp-Spaces. Spaces of Distributions. Introduction to Sobolev Spaces. Elliptic Boundary Value Problems. Solvability of Nonlinear Elliptic Equations. Topological Degree and ItsApplications. Appendix. Solutions and Hints. Notation. References. Index.

Product Details

  • ISBN13: 9780582246942
  • Format: Hardback
  • Number Of Pages: 416
  • ID: 9780582246942
  • weight: 735
  • ISBN10: 0582246946

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