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The Leray-Schauder Degree as Topological Method Solution of Nonlinear Elliptic Equations

Received: 11 August 2017    Accepted: 09 September 2017    Published: 29 October 2017
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Abstract

In the present paper using precise results on the solutions of linear elliptic differential operators with Holder continuous coefficient as well as a variant of the Lery - Schauder method and the gal of this paper to find an adequate degree theory for the infinite dimensional setting and to extend the theory of homotopy classes of maps form to to homotopy classes of maps on infinite dimensional spaces.

DOI 10.11648/j.pamj.20170605.13
Published in Pure and Applied Mathematics Journal (Volume 6, Issue 5, October 2017)
Page(s) 148-153
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

The Leray - Schauder Degree, Elliptic Boundary Value Problem

References
[1] R. C. A. M. Vandervorst, Topological Methods for Nonlinear Differential Equations, April 25, 2008.
[2] R. A. Adams and J. J. Fournier, Sobolev space, 2nd. pure and Applied Mathematics, Vol 140, Elsever/Academic Press, Amsterdam, 2003.
[3] Y. Andre, Series Gevery de type arithnetique I. Theoremes de purete et de dualite, Annals of Mathematics 151, (2000).
[4] L. C. Evans, Partial differential equations, Graduate Studies in Mathematics, Vol 19, American Mathematical Society, Providence, RI, 1998.
[5] Felix E. Browder, Topological Methods for nonlinear Elliptic Equations of Aritary order. Pacific Journal of Mathematics, Vol. 17, n 01. 1966.
[6] J. Cronin, Fixed points and topological degree in nonlinear analysis, Providence, 1964.
[7] F. E. Browder, On the spectral theory of elliptic differential operators, J, Math. Annalen, 142 (1961), 22-130
[8] M. A. Krasnoselski, Topological methods in the theory of nonlinear integral equations, Moscow, 1956 "Trans onto English, Pergamon Press, 1964".
[9] C. Miranda, Equazioni alle Derivate Parziali di Tipo Ellitic, Springer, Berlin, 1955.
[10] L. Nirenberg, Nonlinear elliptic partial differential equations and Holder continuity, Comm, Pure App. Math 6 (1953) 103-157.
[11] J. Schauder, Der Fixpunktsatz in Funktionalraumen, Studia Math. 2 (1930), 171-180.
Author Information
  • Department of Mathematics, Faculty of Sciences, University of Tabuk, Tabuk, Kingdom of Saudi Arabia

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    Nedal Hassan Elbadowi Eljaneid. (2017). The Leray-Schauder Degree as Topological Method Solution of Nonlinear Elliptic Equations. Pure and Applied Mathematics Journal, 6(5), 148-153. https://doi.org/10.11648/j.pamj.20170605.13

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    Nedal Hassan Elbadowi Eljaneid. The Leray-Schauder Degree as Topological Method Solution of Nonlinear Elliptic Equations. Pure Appl. Math. J. 2017, 6(5), 148-153. doi: 10.11648/j.pamj.20170605.13

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    AMA Style

    Nedal Hassan Elbadowi Eljaneid. The Leray-Schauder Degree as Topological Method Solution of Nonlinear Elliptic Equations. Pure Appl Math J. 2017;6(5):148-153. doi: 10.11648/j.pamj.20170605.13

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  • @article{10.11648/j.pamj.20170605.13,
      author = {Nedal Hassan Elbadowi Eljaneid},
      title = {The Leray-Schauder Degree as Topological Method Solution of Nonlinear Elliptic Equations},
      journal = {Pure and Applied Mathematics Journal},
      volume = {6},
      number = {5},
      pages = {148-153},
      doi = {10.11648/j.pamj.20170605.13},
      url = {https://doi.org/10.11648/j.pamj.20170605.13},
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      abstract = {In the present paper using precise results on the solutions of linear elliptic differential operators with Holder continuous coefficient as well as a variant of the Lery - Schauder method and the gal of this paper to find an adequate degree theory for the infinite dimensional setting and to extend the theory of homotopy classes of maps form  to  to homotopy classes of maps on infinite dimensional spaces.},
     year = {2017}
    }
    

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