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Altin, Abdullah

Some expansion formulas for a class of singular partial differential equations. (English) Zbl 0486.35018

Proc. Am. Math. Soc. 85, 42-46 (1982).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0486.35018

Cited in 13 Documents

MSC:

35C05 Solutions to PDEs in closed form
35G05 Linear higher-order PDEs
35C10 Series solutions to PDEs

Keywords:

iterated equation; elliptic and ultrahyperbolic equations; Almansi’s expansion; Kelvin principle; induction method; homogeneous function expansion
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References:

[1] E. Almansi, Sull’ integrazione dell’ differenziale \( {\Delta ^{2m}}u = 0\), Ann. Mat. Ser. II, III (1899), 1-59.
[2] A. Okay Çelebi, On the generalized Tricomi’s equation, Comm. Fac. Sci. Univ. Ankara Sér. A 17 (1968), 1 – 31 (English, with Turkish summary).
[3] Paul Germain and Roger Bader, Sur le problème de Tricomi, Rend. Circ. Mat. Palermo (2) 2 (1953), 53 – 70 (French). · Zbl 0052.09701 · doi:10.1007/BF02871677
[4] Alfred Huber, Some results on generalized axially symmetric potentials, Proceedings of the conference on differential equations (dedicated to A. Weinstein), University of Maryland Book Store, College Park, Md., 1956, pp. 147 – 155. · Zbl 0072.31406
[5] W. Thomson, Extraits de deux lettres adressées a M. Liouville, J. Math. Pures Appl. 12 (1847), 256.
[6] Dorothee Krahn, On the iterated wave equation. IA, IB, Nederl. Akad. Wetensch. Proc. Ser. A 60 = Indag. Math. 19 (1957), 492 – 505. · Zbl 0081.31202
[7] L. E. Payne and W. H. Pell, The Stokes flow problem for a class of axially symmetric bodies, J. Fluid Mech. 7 (1960), 529 – 549. · Zbl 0091.42202 · doi:10.1017/S002211206000027X
[8] Alexander Weinstein, On a class of partial differential equations of even order, Ann. Mat. Pura Appl. (4) 39 (1955), 245 – 254. · Zbl 0065.33102 · doi:10.1007/BF02410772
[9] Alexander Weinstein, On a singular differential operator, Ann. Mat. Pura Appl. (4) 49 (1960), 359 – 365. · Zbl 0094.06101 · doi:10.1007/BF02414059
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