4810 Existence Theorems 



Integrals, continuous and discontinuous. 

 Cauchy, A. L. C. B. 29 (1849) 548-. 



of equation, 1st order, degree. Autonne, . 

 C. B. 118 (1894) 1184-. 



, linear independent, of 1st class, number. 

 Christoffel, E. B. A. Mt. 10 (1880-82) 81-. 



of ordinary equations, initial conditions de- 

 termining. Niccoletti, 0. Tor. Ac. Sc. At. 

 33 (1897) 514- or 746-. 



. , system, unique determination by 



Cauchy 's initial conditions. Painlev$, . 



Par. S. Mth. Bll. 28 (1900) 191-. 

 partial equations, domains of convergence 



for. Koenigsberger, L. Crelle J. Mth. 112 



(1893) 181-. 

 , rational, of Rummer's equation. Goursat, 



E. Mth. A. 24 (1884) 445-. 



of system of total differential equations, 

 convergence of expansions. Meray, , & 

 Eiquier, . Par. EC. Norm. A. 6 (1889) 

 355-; 7 (1890) 23-. 



^ + py = 0, conditions for finiteness. 



dx' 2 



Zukovskij, N. E. Bee. Mth. (Moscou) 16 



(1893) 582-. 

 Integration, complete, of given system of 



ordinary equations, possibility. Lipschitz, R. 



[1868-76] A. Mt. 2 (1868-69) 288-; Bll. 



Sc. Mth. As. 10 (1876) 149-. 

 Irreducibility. Konigsberger, L. Crelle J. Mth. 



92 (1882) 291-. 

 Linear partial equation. Bendixson, I. Par. S. 



Mth. Bll. 24 (1896) 220-. 

 Ordinary equations. Picard, E. Par. S. Mth. 



Bll. 19 (1891) 61-. 

 . Peano, G. N. A. Mth. 11 (1892) 



79-. 

 . Arzela, C. Bologna Ac. Sc. Mm. 6 



(1896-97) 131-. 

 . Lindelof, E. Helsingf. Acta 21 (1896) 



No. 7, 13 pp. 

 Orthoic systems. Eiquier, . C. B. 125 



(1897) 1159. 

 Partial equations. Mie, G. Z. Mth. Ps. 37 



(1892) 151-, 193-. 

 containing any number of functions and 



variables. Darboux, G. C. E. 80 (1875) 



101-. 



. Genocchi, A. 



C. E. 80 (1875) 315-. 



, general demonstration. Me"ray,C. Liouv. 



J. Mth. 6 (1880) 235-. 



, any order. Darboux, G. C. B. 80 

 (1875) 317-. 



Any system. Meray, C. C. E. 80 (1875) 



389-. 

 . Eiquier, . C. B. 114 (1892) 731- ; 



Par. EC. Norm. A. 10 (1893) 65-, 123-, 



167-. 

 System of ordinary equations, order. Jacobi, 



C. G. J. Crelle J. 64 (1865) 297-. 

 partial equations. Goursat, E. Par. S. 



Mth. Bll. 26 (1898) 129-. 

 Systems, cases. Eiquier, . C. E. 125 (1897) 



933-. 

 , most general. Eiquier, C. Par. EC. Norm. 



A. 14 (1897) 99-. 



Solution and Reduction 4820 



Systems of partial equations. Koenigsberger, L. 



Mth. A. 42 (1893) 485-. 

 . Stackel, P. Crelle J. Mth. 119 



(1898) 339-. 

 , priority claim. Delassus, E. Par. EC. 



Norm. A. 14 (1897) 243-. 

 Au=ke u . Picard, E. C. E. 116 (1893) 1015-. 



4820 Methods of solution and re- 

 duction of ordinary differential 

 equations. 



Adjoint equation, and systems of equations. 



Borel, E. Par. EC. Norm. A. 9 (1892) 63-. 

 Algebraic equations. Kimigsberger, L. D. Nf . 



Tbl. (1889) 197-. 

 , 1st order. Vivanti, G. Palermo Cir. 



Mt. Ed. 4 (1890) 9-. 

 , and degree. Voss, A. Mth. A. 23 



(1884) 157-. 

 , roots of which are integrals of Eiccati's 



equation. Autonne, L. Liouv. J. Mth. 6 



(1900) 157-. 



homogeneous equations. Appell, P. C. E. 



104 (1887) 1776-. 



Application of transformation groups. Page, 



J. M. A. Mth. 9 (1894-95) 59-. 

 Applications of calculus of symbols. Russell, 



W. H. L. Phil. Trans. (1861) 69- ; (1862) 



253-; (1863) 517-. 

 Approximate methods. Durand,W.F. A. Mth. 



12 (1898-99) 110-. 

 Behaviour near singular points. Dulac, H. 



C. B. 129 (1899) 276-. 

 Change of dependent and independent variables, 



applications. Niven, C. QJ. Mth. 10 (1870) 



312-. 



independent variable. Thomas, L. N. A. 

 Mth. 9 (1850) 365-. 



. Spitzer, S. C. B. 49 (1859) 48-, 



270-. 

 . Glashan, J. C. Am. J. Mth. 3 



(1880) 190-. 

 . variables, formulae. Fais, A. Bologna 



Ed. (1877) 60-. 

 Clairaut's equation. Mansion, P. [1876] Mess. 



Mth. 6 (1877) 90-. 

 , analogues of. Goursat, E. Par. S. Mth. 



Bll. 23 (1895) 88-. 

 , , of higher order. Raffy, L. Par. 



S. Mth. Bll. 25 (1897) 71-. 

 generalised, and equations of 3 variables. 



Gasparis, A. de. Nap. Ed. 6 (1847) 149-. 

 Cremonian quadratic substitutions, application 



to equations, 1st order. Autonne, L. C. E. 



105 (1887) 929- ; 106 (1888) 262-. 

 Depression of equations. Cunningham, (Lt.- 



Col.) A. Mess. Mth. 17 (1888) 118- ; 18 

 (1889) 122-. 



Determination, explicit, of equations, 2nd order, 

 with fixed critical points. Painleve, P. C. E. 

 126 (1898) 1329-. 



Differential resolvents. Spottiswoode, W. QJ. 

 Mth. 6 (1864) 262-. 



and partial differential resolvents. Raw- 

 son, R. Manch. Lt. Ph. S. P. 21 (1882) 59-. 



357 



