4840 Partial Differential Equations. Second and Higher Orders 4840 



method, graphic. Massau, J. Brux. A. Tr. 



Pbl. 5 (1900) 507-. 

 , Jacobi-Mayer, improvement. Lie, S. Chris- 



tiania F. 15 (1873) 282-. . 

 , Lagrange's, special cases. Serdobinskij , 



V. E. [1889] Eec. Mth. (Moscou) 14 (1890) 



439-; Fschr. Mth. (1890) 351. 

 , Lie's, extension. Mayer, A. C. G. Mth. 



A. 8 (1875) 313-. 



for linear equations, 2nd order, with 2 in- 

 dependent variables. Winckler, A. [1883] 

 Wien Ak. Sb. 88 (1884) (Ab. 2) 7-. 



, Monge- Ampere, extension. Vivanti, G. 



Mil. I. Lomb. Ed. 32 (1899) 506-. 

 , Monge's, for linear equations, 2nd order. 



Laguerre, E. N. A. Mth. 15 (1876) 49-. 

 , new, for Monge-Ampere equation. Lie, M. 



S. Arch. Mth. Ntvd. 2 (1877) 1-. 



for non-linear equations, 2nd order. Winckler, 

 A. Wien Ak. Sb. 89 (1884) (Ab. 2) 614-. 



, Eiemann's, for hyperbolic equations with 



application to vibration problems. Wirtinger, 



W. Mth. A. 48 (1897) 365-. 

 methods for equations, 2nd order, of function 



of 2 variables. Imschenetsky, V. G. Arch. 



Mth. Ps. 54 (1872) 209-. 

 with 2 independent variables. Bur- 



gatti, P. Palermo Cir. Mt. Ed. 12 (1898) 210-. 

 by multiple integrals. Mellin, H. Acta Mth. 



22 (1899) 19-. 

 of simultaneous equations. Aoust, L. Crelle 



J. 47 (1854) 369-. 

 , 2nd order, with 2 independent vari- 



W" 



_ d n z d n z 



+ p _ UP _ n 



" l dxdx n ~* n dy n v ' 

 Tychsen, C. Z. Mth. Ps. 13 (1868) 441-. 

 ffiu d'tt 



~~dx* + df + k "' U:=0 - Weber ' H - C 1868 ] Mth - 

 A. 1 (1869) 1-. 



T~2 + j~~2~ under given conditions as to 



boundary and discontinuity. Schwarz ,H. A. 

 Berl. Mb. (1870) 767-. 



= . Prym, F. E. CreUe J. 73 (1871) 



340-. 

 d n z _,d m+n ;z 



+ x->F m (y). 

 Spitzer, S. Arch. Mth. Ps. 51 (1870) 499-- 



F. Z. Mth. Ps. 28 (1883) 97-. 



Laplace's equations with equal invariants, cer- 

 tain classes. Thybaut, A. C. E. 122 (1896) 

 834-. 



, systems. Tzitztica, G. C. E. 128 

 (1899) 601-. 



, T ^- = a -- + b ~ , class. Tzitzeica, G. 



dxdy dx dy 



Bll. Sc. Mth. 24 (1900) 142-. 



ables. Vdlyi,J. Crelle J. Mth. 95 (1883) 99-. __,_ = _ w ith quadratic solutions. 



, systems. Koenigsberger, L. Mth. A. 



41 (1893) 260-. 

 by symbolic method. Curtis, A. H. Camb. 



and Dubl. Mth. J. 9 (1854) 272-. 

 theory. Lie, M. S. Christiania F. (1880) 



No. 1, 4 pp. 

 for higher partial differential problems. 



Weber, E. von. Leip. Mth. Ps. B. 49 (1897) 329-. 



of -^ = -3^ . Liouville, J. [1836] Par. 6c. 



Pol. J. 25 cah. (1837) 85-. 

 ~ a " 1 T^. = x ~ m j~^i- s P itzer > s - Grunert Arch. 



30 (1858) 335. 



dz 



Spitzer, S. Grunert Arch. 33 (1859) 461. 



- (x+ y)2 r y + m ^ (x +y) T x +m *( x+ ti | 



+ J!2 = 0. Spitzer, S. Grunert Arch. 33 

 (1859) 476- ; 38 (1862) 451-. 

 d*z r fdz\*~\ d*z P. 



Fuchs, L. Crelle J. 58 (1860) 



= . Hoppe, R. [1860] Crelle J. 58 



(1861) 369-. 



-\ ;;=0. Neumann, C. Crelle J. 59 



(1861) 335-. 



2 d n z _ d n z 



dx n dy n ' 



7 (1862) 343-. 



Spitzer, S. Schlomilch Z. 



Tzitzeica, G. C. E. 131 (1900) 487-. 

 Legendre's theory. Combescure, E. C. E. 



74 (1872) 798-. 

 Majorant functions applied to some differential 



systems. Eiquier, . C. E. 125 (1897) 



1018-. 

 Method, Cauchy's, extension to equations, any 



order. Beudon, J. C. E. 121 (1895) 808-. 



of characteristics, general system of equa- 

 tions integrable by. Tedone, O. A. Mt. 1 

 (1898) 283-. 



, Darboux's, application. Beudon, . C. 

 E. 120 (1895) 902-. 



, , to s=f(r, t). Boer, F. de. Amst. 

 Ak. Vs. M. 8 (1891) 221- ; Arch. Neerl. 27 

 (1894) 355-. 



, Laplace's, extension to equations, 3rd and 

 higher orders. Le Roux, . Par. S. Mth. 

 Bll. 27 (1899) 237-. 



, Picard's, extension to equations with 3 vari- 

 ables. Zaremba, S. Prace Mt.-Fiz. 9 (1898) 



of successive approximations, and theory of 

 equations. Picard, E. Liouv. J. Mth. 6 

 (1890) 145-, 231. 



Methods of Eiemann and Picard, extension 



to a class of equations. Niccoletti, 0. Nap. 



Ac. At. 8 (1897) No. 2, 22 pp. 

 Monge-Ampere equation, equations of 2nd order 



analogous to. Goursat, E. Par. S. Mth. 



Bll. 27 (1899) 1-. 

 equations, certain. Clairin, J. C. E. 



130 (1900) 997-. 



373 



