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

Nedal Hassan Elbadowi Eljaneid

doi:doi:10.11648/j.pamj.20170605.13

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

Nedal Hassan Elbadowi Eljaneid

Published in Pure and Applied Mathematics Journal (Volume 6, Issue 5)

Received: 11 August 2017 Accepted: 9 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.

Published in	Pure and Applied Mathematics Journal (Volume 6, Issue 5)
DOI	10.11648/j.pamj.20170605.13
Page(s)	148-153
Creative Commons	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), 2017. 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, 2^nd. 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.

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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},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20170605.13},
  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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TY  - JOUR
T1  - The Leray-Schauder Degree as Topological Method Solution of Nonlinear Elliptic Equations
AU  - Nedal Hassan Elbadowi Eljaneid
Y1  - 2017/10/29
PY  - 2017
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T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
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AB  - 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.
VL  - 6
IS  - 5
ER  -

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Author Information

Nedal Hassan Elbadowi Eljaneid

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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ACS 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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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

Copy | Download

@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},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20170605.13},
  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}
}

Copy | Download

TY  - JOUR
T1  - The Leray-Schauder Degree as Topological Method Solution of Nonlinear Elliptic Equations
AU  - Nedal Hassan Elbadowi Eljaneid
Y1  - 2017/10/29
PY  - 2017
N1  - https://doi.org/10.11648/j.pamj.20170605.13
DO  - 10.11648/j.pamj.20170605.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 148
EP  - 153
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20170605.13
AB  - 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.
VL  - 6
IS  - 5
ER  -

Copy | Download