Some Basic Tools

  • Alain HarauxEmail author
  • Mohamed Ali Jendoubi
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


Throughout the book we rely on various tools and general concepts which are explicited once and for all in this chapter: some lemmas on differential and integral inequalities, a uniformization lemma for Łojasiewicz type inequalities, the definition and main properties of semi-Fredholm operators and analytic maps from a Banach space to another.


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    E.A. Coddington, N. Levinson, Theory of Ordinary Differential Equations (McGraw-Hill Book Company Inc., New York, 1955)zbMATHGoogle Scholar
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    T.I. Zelenyak, Stabilization of solutions of boundary value problems for a second-order parabolic equation with one space variable. (Russian) Differencialnye Uravnenija 4, 34–45 (1968)zbMATHGoogle Scholar
  3. 3.
    H. Brézis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext (Springer, New York, 2011)Google Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Laboratoire Jacques-Louis LionsSorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7598ParisFrance
  2. 2.Institut Préparatoire aux Etudes Scientifiques et TechniquesUniversité de CarthageLa MarsaTunisia
  3. 3.Faculté des sciences de Tunis, Laboratoire EDP-LR03ES04Université de Tunis El ManarTunisTunisia

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