Nonlinear partial differential equations: sequential and weak solutions

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Page iii

Copyright page
Page iv

Dedicated
Page v

Foreword
Pages vi-vii

Preliminaries
Pages viii-xii

Notation
Page xix

Note to the Reader
Page xviii

Chapter 1 Sequential Solutions of Nonlinear PDEs
Pages 1-36

Chapter 2 Necessary and/or Sufficient Conditions for the Existence of Sequential Solutions
Pages 37-63

Chapter 3 Algebras Containing the Distributions
Pages 65-119

Chapter 4 Resolution of Singularities of weak Solutions for Polynomial Nonlinear PDEs
Pages 121-162

Chapter 5 Stability and Exactness of Sequential and Weak Solutions for Polynomial Nonlinear PDEs
Pages 163-172

Chapter 6 Characterization of the Necessary Structure of the Algebras Containing the Distributions
Pages 173-198

Chapter 7 Quantum Scattering in Potentials Positive Powers of the Dirac & Distribution
Pages 199-222

Chapter 8 Products with Dirac & Distributions
Pages 223-250

Chapter 9 Linear Independent Families of Dirac & Distributions at a Point
Pages 251-264

Chapter 10 Support and Local Properties
Pages 265-283

Appedix 1 Neutrix Calculus and Negligible Sequences of Functions
Pages 285-288

Appendix 2 The Embedding Impossibility Result of L. Schwartz
Pages 289-292

Appendix 3 A Nonlinear Extension of the Lax-Richtmyer Equivalence between Stability and Convergence of Difference Schemes
Pages 293-300

Appendix 4 The Cauchy-Bolzano Quotient Algebra Construction of the Real Numbers
Pages 301-304

References
Pages 305-317