4810 



Differential Equations. Existence Theorems 



4810 



Solution. De Morgan, A, [1856] Camb. Ph. 



S. T. 10 (1864) 21-. 



, influence of reality and continuity condi- 

 tions on. Christo/el, E. B. Crelle J. 66 



(1866) 1-. 

 System, degree of generality. Riquier, . C. 



E. 130 (1900) 162-. 

 Systems and their connexion with partial 



linear equations. Jacobi, C. G. J. Crelle J. 



23 (1842) 1-. 

 of infinite order. Koch, H. von. Stockh. 



Ofv. (1899) 395-. 

 , theory. Stodolkievitz , A. J. C. E. 120 



(1895) 36-, 595-. 



, transformations. Delassus, E. C. E. 123 



(1896) 1246-. 



Theory. Schmidten, H. G. Kiob. Ov. (1818- 



19) 6-. 



. Jacobi, C. G. J. Crelle J. 17 (1837) 68-. 

 . Serret, J. A. C. E. 19 (1844) 910-. 

 . Anisimov, V. A. Vars. S. Nt. Tr. 



(C. R., Ps. C.) No. 6, 2-. 

 , general. Picard, E. Bll. Sc. Mth. 11 



(1887) 194-. 

 Tracing of curves from differential equations. 



Coriolis, G. Liouv. J. Mth. 1 (1836) 5-. 

 Transformation of the general integral of the 



characteristic equation ; etc. Cauchy, A. L. 



C. E. 29 (1849) 103-. 



4810 Existence theorems for ordi- 

 nary and partial differential 

 equations. 



Cauchy, A. L. C. E. 14 (1842) 1020-. 

 Jablonski, E. As. Fr. C. E. (1877) 198-. 

 Lerch, M. Prag Sb. (1889) 1 (Mth.-Nt.) 180-. 

 Lichtenfels, 0. von. Mh. Mth. Ps. 1 (1890) 



275-. 

 Sincov, D. Kazan S. Ps.-Mth. Bll. 3 (1893) 



138-. 

 Osgood, W. F. N. Y. Am. Mth. S. Bll. 4 (1898) 



291, 292-. 

 Cauchy ' s existence theorem . Koenigsberger , L . 



Crelle J. Mth. 104 (1889) 174-. 

 , Poincare's extension. Koenigsberger, 



L. Crelle J. Mth. 113 (1894) 115-. 

 Complete integral for f(x, y, y') = 0, demon- 

 stration. Zeuthen, H. G. (xii) Ts. Mth. 4 



(1880) 161-. 



Differential relations soluble without integra- 

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Ac. Sect. Sc. 7 (1867-71) 447-. 

 resolvents. Cockle, (Sir) J. [1864] Manch. 



Lt. Ph. S. P. 4 (1865) 38-. 

 Equations having complete algebraic integrals, 



etc. Hill, C. J. D. Crelle J. 25 (1843) 



38. 

 Existence of first integrals of partial equations, 



2nd order. Brioschi, F. Tortolini A. 5 



(1854) 268-; 6 (1855) 426- 

 integrals of partial system, determined 



by initial conditions. Eiquier, . C. E. 



126 (1898) 208-. 

 Finite number of singular points, Fuchs's 



theorem. Poincar6,H. C. E. 99 (1884) 75-. 



Highest power of -r-j-; in nth derivative of 



fix, j/) = 0. Zeuthen, H. G. Mth. Ts. 1 

 (1859) 40-. 



Homogeneous linear equation. Hamburger, M. 

 Crelle J. Mth. 118 (1897) 351-. 



(Hamburger). Fuchs, L. Crelle 

 J. Mth. 118 (1897) 354-. 



---- . Gutzmer, A. Crelle J. Mth. 119 

 (1898) 82-. 



Integrdbility, 



conditions. C., B. D. (vi Adds.) Gergonne 

 A. Mth. 14 (1823-24) 319-. 



. Joachimsthal, F. [1844] Crelle J. 33 

 (1846) 95-. 



. Letnikow, A. Z. Mth. Ps. 12 (1867) 223-. 



. Laurent, H. N. A. Mth. 6 (1887) 19-. 



for differential and finite difference equa- 

 tions. Minich, S. R. Tortolini A. 1 (1850) 

 321-. 



--- functions. Sarrus, F. Gergonne A. 



Mth. 14 (1823-24) 197-. 

 ---- . Bertrand, J. Par. EC. Pol. J. 



28" cah. (1841) 249-; Liouv. J. Mth. 14 



(1849) 123-. 

 ---- . Sarrus, F. C. E. 28 (1849) 



439-. 

 ---- , several variables. Dirksen, E. H. 



Berl. Ab. (1836) 79-. 

 , equations which do not satisfy. Paoli, P. 



Verona S. It. Mm. 6 (1792) 501-. 



for linear equations, of 1st order, n variables. 

 Deahna, F. Crelle J. 20 (1840) 340-. 



-- partial equation, 1st order. Schultz, E. 

 Arch. Mth. Ps. 13 (1895) 311-. 



Svanberg, A. F. Stockh. Ofv. 5 (1848) 

 155-. 



-- 4>3 (*) y" + 02 (*) y' + 0i (*) y = o. svan- 



berg, A. F. Ups. N. Acta S. Sc. 1 (1851) 1-. 

 criteria. Minich, S. R. Yen. At. 2 (1843) 377-. 



. Challis, J. Ph. Mg. 24 (1844) 94-. 



. Volpicelli, P. Em. At. 4 (1850-51) 622. 

 criterion, Euler's, reduction of conditions to 



single equation. Winckler, A. [1883] Wien 



Ak. Sb. 88 (1884) (Ab. 2) 820-. 

 factor, means of determining. Maximovitch, W. 



C. E. 97 (1883) 1544-. 

 immediate, of differential expression, any order, 



conditions. Pujet, A. C. E. 82 (1876) 



740-. 

 and integration. Combescure, E. [1871] A. 



Mt. 5 (1871-73) 20-. 

 of ordinary equations. Peano, G. Mth. A. 



37 (1890) 182-. 



--- . Me, G. Mth. A. 43 (1893) 553-. 

 --- . Arzela, C. Bologna Ac. Sc. Mm. 5 



(1895-96) 257-. 



Integrals, algebraic, of Rummer's equation. 



Goursat, E. C. E. 103 (1886) 993- ; Liouv. 



J. Mth. 3 (1887) 255-. 

 of 1st class, representation by fundamental 



system. Hensel.K. Crelle J. Mth. 117 (1897) 



29-. 



356 



