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The Lane-Emden Function and Nonlinear Eigenvalues Problems

Ould Ahmed Izid Bih Isselkou[1]

  • [1] Faculté des Sciences et Techniques, B.P. 5026 Nouakchott, Mauritanie

Annales de la faculté des sciences de Toulouse Mathématiques (2009)

  • Volume: 18, Issue: 4, page 635-650
  • ISSN: 0240-2963

Abstract

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We consider a semilinear elliptic eigenvalues problem on a ball of ℜ n and show that all the eigenfunctions and eigenvalues, can be obtained from the Lane-Emden function.

How to cite

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Isselkou, Ould Ahmed Izid Bih. "The Lane-Emden Function and Nonlinear Eigenvalues Problems." Annales de la faculté des sciences de Toulouse Mathématiques 18.4 (2009): 635-650. <http://eudml.org/doc/10121>.

@article{Isselkou2009,
abstract = {We consider a semilinear elliptic eigenvalues problem on a ball of $\Re ^\{n\}$ and show that all the eigenfunctions and eigenvalues, can be obtained from the Lane-Emden function.},
affiliation = {Faculté des Sciences et Techniques, B.P. 5026 Nouakchott, Mauritanie},
author = {Isselkou, Ould Ahmed Izid Bih},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
month = {10},
number = {4},
pages = {635-650},
publisher = {Université Paul Sabatier, Toulouse},
title = {The Lane-Emden Function and Nonlinear Eigenvalues Problems},
url = {http://eudml.org/doc/10121},
volume = {18},
year = {2009},
}

TY - JOUR
AU - Isselkou, Ould Ahmed Izid Bih
TI - The Lane-Emden Function and Nonlinear Eigenvalues Problems
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2009/10//
PB - Université Paul Sabatier, Toulouse
VL - 18
IS - 4
SP - 635
EP - 650
AB - We consider a semilinear elliptic eigenvalues problem on a ball of $\Re ^{n}$ and show that all the eigenfunctions and eigenvalues, can be obtained from the Lane-Emden function.
LA - eng
UR - http://eudml.org/doc/10121
ER -

References

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  9. Isselkou (O.A.-I.-B.).— Supercritical Elliptic Problems on Domains of ℜ N , in Progress in P.D.E: The Metz Survey, Pitman 296, p. 172-185 (1993). Zbl0806.35036MR1248644
  10. Joseph (D.D.) and Lundgren (T.S.).— Quasilinear Dirichlet Problems Driven by Positive Sources, Arch. Rational Mech. Anal. 49, p. 241-269 (1972/1973). Zbl0266.34021MR340701
  11. Keener (J.) and Kelle (H.).— Positive Solutions of Convex Nonlinear Eigenvalue Problems, J. Diff. Eq. 16, p. 103-125 (1974). Zbl0287.35074MR346305
  12. Keller (H.B.).— Some Positone Problems Suggested by the Nonlinear Heat Generation, in “Bifurcation Theory and Nonlinear Eigenvalues Problems,” W.A. BENJAMIN, INC., (1969). Zbl0187.03901
  13. Loewner (C.) and Nirenberg (L.).— Partial Differential Equations Invariant under Conformal or Projective transformation. Contribution to Analysis (L. Ahlfors ed.) Academic Press N.Y. p. 245-272, (1974). Zbl0298.35018MR358078
  14. Pohozaev (S.I.).— On Entire Solutions of Semilinear Elliptic Equations. Research Note Math. 266, Pitman, p. 56-69, London (1992). Zbl0821.35046MR1194215
  15. Sachdev (P.L.).— Nonlinear Ordinary Differential Equations and Their Applications, Pure and Applied Mathematics, Number 142. Zbl0722.34001

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