Факторизация и преобразования дифференциальных уравнений - Беркович Л.М.
ISBN 5-93972-154-0
Скачать (прямая ссылка):
Reseach Report 1, January 1997. [303] Euler N., Steeb W.-H., Gurus K. On exact solution for damped
anharmonic oscillators. J. Phys. A: Math. Gen., 1989, 22, Е195ЛЛ99. [304] Fayet J. Invariants de quelques equations differentielles et reduction du
celle-ci a des equations a coefficients constants. These, Paris, 1937, 81 p. [305] Fayet J. Sur la reduction des equations differentielles lineaires et
homogenes a des equations a coefficients constants. Comptes Rendus,
Paris, 1937, t. 204, N 9, p. 650-692. [306] File P.C. Asymptotic states for equations of reaction and diffusion.
Bull. AMS, 1978, 84, N 5, p. 693-726. [307] File P.C. Mathematical aspects of reacting and diffusing systems.
Berlin, Springer, 1979. [308] Fisher R.A. The wave of advance of advantageous genes. Annals of
Eugenics, 1937, 7, p. 355-369. [309] Floquet G. Sur la theorie des equations differentielles lineaires.
Ann. Sei. de ГЁс. Norm., 1879, t. 8., Supplement. 2 ser. p. 132. [310] Forsyth A.R. Invariants, covariants and quotient-derivatives
associated with linear differential equations. Phylosophycal Trans, of the
Royal Society of London, 1899, A, t. 179, p. 377^189.
[311] Frobenius G. Uber den Begriff der Irreductibilitat der Theorie linearen Differentialgleichungen. J. Reine Angew. Math., 1873, vol. 76, s. 236-270.
[312] Gambier B. Sur les equations differentielles du second ordre et du premier
degre dont l'integrale generale est a points critiques fixes. These, Paris
(1909); Acta Math., 33 (1910), p. 1-55. [313] Gardner CS., Greene J.M., Kruskal M.D., Miura R.M. A method for
solving the Korteweg-de Vries equation. Physical Rews Letters, 1967, t.
19, p. 1095-1097.
[314] Govinder K.S., Athorne C, and Leach P.G.L. The algebraic structure of generalized Ermakov systems in three dimensions. J. Phys. A: Math. Gen., 1993, 26, p. 4035-4046.
[315] Grammatikos B., Moulin-Ollagnier J., Ramani A., Strelcyn J.-M., Wojciechowski S. Integrals of quadratic ordinary differential equations in R3.- The Lotka-Volterra system. Physica A, 163, 1990, p. 683-722.
Литература
447
Gregus М. Linearna differencialna rovnica tretieho radu. Veda. Bratislava, 1981.
Gylden H. Die bahnbewegungen in einem Systeme von zwei Korpern in dem fall, das die massen Veranderungen unterworfen sind. Astron. Nachr., 1884, 109, p. 2593-2594.
Hadjidemetriou J. Secular variation of mass of binary systems. Advances in Astronomy and Astrophysics, N.Y.-London, Acad. Press, 1967, p. 131-188.
Halphen G.H. Memoire sur la reduction des equations lineaires differentielles aux formes integrables. Memoires presentes par divers savants а Г Acad. des. Sei. de l'inst. mat. de France, 1884, Т. 23, N 1, 301 p.
Halphen G.H. Sur les invariants des equations differentielles lineaires du quatrieme ordre. Acta Math. 3 (1883/1884), p. 325-380. Halphen G.H. Sur une classe des equations differentielles lineaires. Comptes Rendus, Paris, 1881, t. 92, p. 779. Hamel G. Lineare Differentialgleichungen mit periodishen Koeffizienten. Math. Ann., 1913, Bd. 73, s. 381.
Heading J. Transformations between second order linear differential equations... Proc. Roy. Edinburg, 1977, A 79, N 1-2, p. 87-105. Hille E. A note on quadratic systems. Proc. Roy. Soc. Edinburgh, 1979, A 72, N l,p. 17-37.
Husty Z. Die Iteration homogenen linearer Differentialgleichungen. Publ. Fac. Sei. Univ. J.E. Purkyne (Brno), 1964, vol. 449, p. 23-56. Ibragimov N.H. Introduction to modern group analysis. Tau, Ufa, 2000. Inselberg A. Phase-plane solutions of Langmuir's equation. J. Math. Anal, and Applic. 1969, vol. 26, N 2, p. 438^146.
Iwinsky T. The generalized eguations of Riccati and their applications to the theory of linear differential eguations. Rozprawy matematyczne, XIII, 1961. 50 p., Warszawa, 1961.
Janet M. Sur les systems d'equations aux derives partielles. J.Math., 1920, vol. 3, p. 65-151.
Jeans J.H. Cosmogonic problems associated with a secular decrease of mass. Monthly Notices Roy. Astron. Soc, 1924, vol. 85, N 1, p.2 . Kakeya S. On linear differential Equation which admits a linear Differential Transformation. Proc. Phys. Math. Soc. Japan, 1938, 20, N 4, p. 365.
Koenigsberger L. Allgemeine Untersuchungen aus der Theorie der Differentialgleichungen. Leipzig, 1882.
448
Литература
[333] Korteweg DJ., de Vries G. On the change of form of long waves advancing in rectangular canal and a new type of long stationary waves. Philos. Magazine and Journal of Science. Series 5, vol. 39, N 241, 1895, p. 422-443.
Krall A.M. Self-adjoint differential expressions of odd order. Amer. Math. Monthly, vol. 73, N 4, 1966, p. 61-62.
Krall H.L. Self-adjoint differential expressions. Amer. Math. Monthly, vol. 67, N 9, 1960, p. 876-878.
Kolchin E.R. Differehtial algebra ahd algebraic groups. N. Y., 1973.
Kovacic J. A Eisenstein criterion for noncommutative polynomials. Proc. Amer. Math. Soc, 1972, vol. 34, N 1, p. 25-29.