Note on a theorem of Avakumović

Author:
J. L. Geluk

Journal:
Proc. Amer. Math. Soc. **112** (1991), 429-431

MSC:
Primary 34E05; Secondary 26A12

DOI:
https://doi.org/10.1090/S0002-9939-1991-1052570-5

MathSciNet review:
1052570

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A short proof is given of a result due to Avakumović. More specifically the asymptotic behavior of the solution of the differential equation in case is given.

**[1]**V. G. Avakumović,*Sur l'équation différentielle de Thomas-Fermi*, Publ. Inst. Math. (Beograd)(N. S.)**1**(1947), 101-113. MR**0028491 (10:455c)****[2]**A. A. Balkema, J. L. Geluk, and L. de Haan,*An extension of Karamata's Tauberian theorem and its connection with complementary convex functions*, Quart. J. Math. Oxford Ser. (2)**30**(1979), 385-416. MR**559046 (80m:40005)****[3]**N. H. Bingham, C. M. Goldie, and J. L. Teugels,*Regular variation*, Cambridge Univ. Press, Cambridge, 1987. MR**898871 (88i:26004)****[4]**J. L. Geluk and L. de Haan,*Regular variation, extensions and Tauberian theorems*, CWI tract 40, Amsterdam, 1987. MR**906871 (89a:26002)****[5]**V. Marić and M. Tomić,*Asymptotic properties of solutions of the equation*, Math. Z.**149**(1976), 261-266. MR**0437864 (55:10785)****[6]**-,*Regular variation and asymptotic properties of solutions of nonlinear differential equations*, Publ. Inst. Math. (Beograd) (N. S.)**21**(1977), 119-129. MR**0508433 (58:22774)****[7]**-,*Asmptotic properties of solutions of a generalized Thomas-Fermi equation*, J. Differential Equations**35**(1980), 36-44.**[8]**E. Omey,*Regular variation and its applications to second order linear differential equations*, Bull. Soc. Math. Belg. Sér. B**33**(1981), 207-229. MR**682648 (84d:34028)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
34E05,
26A12

Retrieve articles in all journals with MSC: 34E05, 26A12

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1052570-5

Article copyright:
© Copyright 1991
American Mathematical Society