4840 Partial Differential Equations. Second and Higher Orders 4840 



class. Kiirschdk,J. Mth. Termt. Ets. 15 (1897) 



225- ; Mth. Nt. B. Ung. 14 (1898) 285-. 

 , including Laplace's equation. Hearn, G. 



W. Phil. Trans. (1846) 133-. 

 , reduction. Oster, B. Arch. Mth. Ps. 



17 (1900) 321-. 

 form f(r, s, t) = 0. Guldberg, A. N. Ts. 



Mth. 10 (B) (1899) 82- ; Fschr. Mth. (1899) 



324. 

 having general first integral. Tanner, H. W. 



L. [1877] Mess. Mth. 7 (1878) 89-. 

 highest differential coefficient appearing in 



linear form. Liouville, B. C. B. 98 (1884) 



216-. 

 integrable by ordinary differential equations. 



Weber, E. van. Munch. Ak. Sb. 26 (1897) 



425-. 

 linear. Engel, F. Leip. Mth. Ps. B. 34 (1882) 



39-. 



. Liouville, R. .C..B..98 (1884) 569-, 704. 

 . Bianchi, L. Km. B. Ac. Line. Rd. 5 



(1889) (Sem. 2) 35-. 

 -^-. Du Bois-Reymond, P. Crelle J, Mth. 104 



(1889) 241-. 

 . Krukovskij, A. L [1894] Eec. Mth. 



(Moscou) 17 (1895) 759- ; Fschr. Mth. (1895) 



393-. 



. Petot, A. C. E. 119 (1894) 510-. 

 . Picard, E. Bll. Sc. Mth. 23 (1899) 150-. 

 , cases. Levy, L. C. E. 100 (1885) 98-; 



Par. EC. Pol. J. 56 (1886) 63-. 

 , . Le Roux, J. C. E. 123 (1896) 1052-. 

 , . Guichard, G. C. B. 131 (1900) 100-. 

 , class. Picard, E. Acta Mth. 12 (1889) 



323-. 

 , with constant coefficients. Coulon, J. C. 



E. 130 (1900) 765-. 

 , general. Paoli, P. [1802] Mod. S. It. Mm. 



10 (1803) 249-. 

 , theorem. Picard, E. C. E. 107 (1888) 



939-. 

 , invariants belonging to. Burgatti, P. 



Em. E. Ac. Line. Ed. 5 (1896) (Sem. 2) 433-. 

 , one parameter, case. Horn, J. Mth. A. 



52 (1899) 271-. 

 , system. Liouville, R. C. B. 104 (1887) 



1496-. 

 , with 2 independent variables. Le Roux, J. 



Par. EC. Norm. A. 12 (1895) 227-. 

 , , theory. Pfannenstiel, E. 



[1882] Ups. S. Sc. N. Acta 11 (1883) (No. 9) 



86pp. 

 , variables. Cotton, E. C. B. 123 



(1896) 936-; 124 (1897) 744-. 

 methods of Charpit and Lagrange. Mainardi, 

 G. Mil. G. I. Lomb. 9 (1856). 94-. 

 point invariants. Medolaghi,P. Em. E. Ac. 



Line. Ed. 6 (1897) (Sem. 2) 247-, 313-. 

 simultaneous, with 3 variables. Weber, E. 

 . van. Munch. Ak. Sb. 25 (1896) 101-. 

 soluble by differentiation. Tanner, H. W. L. 



[1876] Mess. Mth. 6 (1877) 32-. 

 system. Niccoletti, 0. Em. B. Ac. Line. Ed. 



4 (1895) (Sem. 1) 197-. 



with 2 independent variables. Konig, J. 

 Mth. A. 24 (1884) 465-. 



, , theory. Levy, H. C. E. 75 



(1872) 1094-. 



-r 3 independent variables. Vivanti, G. Mth. 

 A. 48 (1897) 474-, 608. 



and 3rd order, linear, with 2 independent vari- 

 ables. Picart, A. N. A. Mth. 2 (1883) 34-. 



higher orders. Falk, M. Ups. Arsk. (1875) 

 40pp. 



Higher orders. 



3rd order. Guldberg, A. Christiania Skr. 

 (Mth.-Nt. Kl.) (1900) No. 5, 43 pp. 



, admitting an intermediate integral. 

 Guldberg, A. C. B. 130 (1900) 1452-. 



, case. Tonelli, A. Em. E. Ac. Line. 

 Ed. 4 (1888) (Sem. 2) 458-. 



, linear, with 3 variables. Fries, J. de. 

 N. Arch. Wisk. 10 (1884) 66-. 



, of orthogonal systems of surfaces. 

 Ltvy, M. C. E. 77 (1873) 1435-. 



and higher orders, linear. Moon, R. Ph. 

 Mg. 21 (1886) 63-. 



4th order. Somigliana, C. A. Mt. 18 (1890) 



59-. 



. Fredholm,!. Stockh. Ofv. (1899) 935-. 



higher order. Gutzmer, A. Liouv. J. Mth. 6 



(1890) 405-. 

 , extension of Biemann's method to. De- 



lassus, . C. B. 117 (1893) 510-. 

 , with intermediate first integrals. Back- 



lund, A. V. [1876] Mth. A. 9 (1877) 199- ; 



13 (1878) 69-. 

 any order. Davidov, A. Y. [1865] (xn) Bee. 



Mth. (Moscou) [1] (1866) 351-. 

 , and their reduction to linear system of 



1st order. Cauchy, A. L. C. E. 15 (1842) 



131-. 

 , any number of variables. Backlund, 



A. V. Lund Un. Acta 12 (1875-76) (Mth., 

 No. 2) 4 pp. 



, theory, general. Lie, S. Leip. Mth. Ps. 



B. 47 (1895) 53-. 



?ith order, class. Tonelli, A. Em. E. Ac. 



Line. Ed. 5 (1889) (Sem. 1) 178-. 

 , formulae relative to. Tonelli, A. Bm. 



E. Ac. Line. Ed. 5 (1889) (Sem. 1) 508-. 



of potential. Picard, E. C. E. 90 (1880) 601-. 

 satisfied by concomitants of quantics. For- 



syth, A.R. L. Mth. S. P. 19 (1889) 24-. 

 certain definite integrals. Torelli, G. 



Nap. Bd. 29 (1890) 123-. 

 similar to those of hydrodynamics, general 



properties. Craig, T. [1881] Am. Ac. Mm. 



10 (Pt. 2) (1882) 362-. 

 simultaneous. Folkierski, W. Par. T. Nauk 



Sc. Pam. 3 (*1873) 1-; Bll. Sc. Mth. As. 6 



(*1874) 156-. 

 . Dixon, A. C. [1899] Phil. Trans. (A) 



195 (1901) 151-. 

 .linear. Painleve,. C. E. 104(1887)1497-. 



systems, in involution. Goursat, E. C. E. 122 , , cases. Appell, P., & Picard, . C. B. 



(1896) 1258-. 92 (1881) 692-. 



with 2 independent variables. Moutard, T. , theory. Campbell, J. E. [1898] L. Mth. 



C. R. 70 (1870) 834-. S. P. 31 (1900) 235-. 



370 



