We consider a semilinear elliptic eigenvalues problem on a ball of and show that all the eigenfunctions and eigenvalues, can be obtained from the Lane-Emden function.
Nous considérons un problème aux valeurs propres, semi-linéaire elliptique, sur une boule de et montrons que ces valeurs et fonctions propres peuvent s’obtenir à partir de la fonction de Lane-Emden.
@article{AFST_2009_6_18_4_635_0,
author = {Ould Ahmed Izid Bih Isselkou},
title = {The {Lane-Emden} {Function} and {Nonlinear} {Eigenvalues} {Problems}},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {635--650},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 18},
number = {4},
year = {2009},
doi = {10.5802/afst.1218},
mrnumber = {2590382},
zbl = {1180.35401},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1218/}
}
TY - JOUR AU - Ould Ahmed Izid Bih Isselkou TI - The Lane-Emden Function and Nonlinear Eigenvalues Problems JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2009 SP - 635 EP - 650 VL - 18 IS - 4 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1218/ DO - 10.5802/afst.1218 LA - en ID - AFST_2009_6_18_4_635_0 ER -
%0 Journal Article %A Ould Ahmed Izid Bih Isselkou %T The Lane-Emden Function and Nonlinear Eigenvalues Problems %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2009 %P 635-650 %V 18 %N 4 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1218/ %R 10.5802/afst.1218 %G en %F AFST_2009_6_18_4_635_0
Ould Ahmed Izid Bih Isselkou. The Lane-Emden Function and Nonlinear Eigenvalues Problems. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 18 (2009) no. 4, pp. 635-650. doi : 10.5802/afst.1218. https://afst.centre-mersenne.org/articles/10.5802/afst.1218/
[1] Chandrasekhar (S.).— An Introduction to the Study of Stellar Structure, University of Chicago Press, Chicago(1939). | Zbl
[2] Crandall (M. G.) and Rabinowitz (P.H.).— Some Continuation and Variational Methods for Positive Solutions of Nonlinear Elliptic Eigenvalue Problems, Arch. Rational Mech. Anal. 58, p. 207-218 (1975). | MR | Zbl
[3] Gidas (B.), Ni (W.-M.) and Nirenberg (L.).— Symmetry and Related Properties via the Maximum Principle, Comm. Math. Phys. 68, p. 209-243 (1979). | MR | Zbl
[4] Gidas (B.) and Spruck (J.).— Global and Local Behavior of Positive Solutions of Nonlinear Elliptic Equations, Comm. Pure Appl. Math., Vol. 34, p.525-598 (1981). | MR | Zbl
[5] Goenner (H.) and Havas (P.).— Exact Solutions of the Generalized Lane-Emden Equation, J. Math. Phys., Vol. 41, Number 10, p.729-742 (2000). | MR | Zbl
[6] Horedt (G.P.).— Approximate Analytical Solutions of the Lane-Emden Equation in dimensional Space, Astron. Astrophys., 172, p. 359-367 (1987). | MR | Zbl
[7] Isselkou (O.A.-I.-B.).— Critical Boundary Constants and Pohozaev Identity, Ann. Fac. Sc. Toulouse, , 10, p. 347-359 (2001). | Numdam | MR
[8] Isselkou (O.A.-I.-B.).— Critical Eigenvalues for a Nonlinear Problem, Nonl. Diff. Eq. Appl., 11, p. 225-236 (2004). | MR
[9] Isselkou (O.A.-I.-B.).— Supercritical Elliptic Problems on Domains of , in Progress in P.D.E: The Metz Survey, Pitman 296, p. 172-185 (1993). | MR | Zbl
[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). | MR | Zbl
[11] Keener (J.) and Kelle (H.).— Positive Solutions of Convex Nonlinear Eigenvalue Problems, J. Diff. Eq. 16, p. 103-125 (1974). | MR | Zbl
[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). | Zbl
[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). | MR | Zbl
[14] Pohozaev (S.I.).— On Entire Solutions of Semilinear Elliptic Equations. Research Note Math. 266, Pitman, p. 56-69, London (1992). | MR | Zbl
[15] Sachdev (P.L.).— Nonlinear Ordinary Differential Equations and Their Applications, Pure and Applied Mathematics, Number 142. | Zbl
Cited by Sources: