We give some fundamental solutions of a class of iterated elliptic equations including Laplace equation and its iterates.
@article{bwmeta1.element.doi-10_2478_BF02475920, author = {Ay\c seg\"ul \c Cetinkaya and Nuri \"Ozalp}, title = {Radial-type complete solutions for a class of partial differential equations}, journal = {Open Mathematics}, volume = {3}, year = {2005}, pages = {508-515}, zbl = {1122.35300}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475920} }
Ayşegül Çetinkaya; Nuri Özalp. Radial-type complete solutions for a class of partial differential equations. Open Mathematics, Tome 3 (2005) pp. 508-515. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475920/
[1] E. Almansi: “Sulle integrazione dell'equazione differenziale Δ2n =0”, Ann. Math. Pura Appl., Vol. 2, (1898), pp. 1–51.
[2] A. Altin: “Some expansion formulas for a class of singular partial differential equations”, Proc. Am. Mat. Soc., Vol. 85(1), (1982), pp. 42–46. http://dx.doi.org/10.2307/2043278 | Zbl 0486.35018
[3] A. Altin: “Solutions of type r m for a class of singular equations”, Inter. J. Math. and Math. Sci., Vol. 5, (1982), pp. 613–619. http://dx.doi.org/10.1155/S0161171282000593 | Zbl 0492.35003
[4] A. Altin: “Radial type solutions for a class of third order equations and their iterates”, Math. Slovaca, Vol. 19(2), (1999), pp. 183–187. | Zbl 0959.35129
[5] L.N. Lyakhov and A.V. Ryzhkov: “Solutions of the B-polyharmonic equation”, Differential Equations, Vol. 36(10), (2000), pp. 1507–1511; Translated from: Differetsial'nye Uravneniya, Vol. 36(10), (2000), pp. 1365–1368. http://dx.doi.org/10.1007/BF02757391 | Zbl 1003.31002
[6] N. Özalp: “ r m -type solutions for a class of partial differential equations”, Commun. Fac. Sci. Univ. Ank. Series A1, Vol. 49, (2000), pp. 95–100. | Zbl 0999.35035
[7] N. Özalp and A. Çetinkaya: “Expansion formulas and Kelvin principle for a class of partial differential equations”, Mathematica Balkanica, New Series, Vol. 15, (2001), pp. 220–226. | Zbl 1090.35518
[8] N Özalp and A. Çetinkaya: “Radial solutions of a class of iterated partial differential equations”, Czechoslovak Mathematical Journal, Vol. 55(2), (2005), pp. 531–541. http://dx.doi.org/10.1007/s10587-005-0044-7 | Zbl 1081.35006
[9] A. Altin-A. Erençin: “Some solutions for a class of singular equations”, Czechoslovak Mathematical Journal, Vol. 54(4), (2004), pp. 969–979. http://dx.doi.org/10.1007/s10587-004-6445-1 | Zbl 1080.35011