About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

First Page Preview
Ďurikovič, Vladimír
On the existence and the uniqueness of solutions and on the convergence of successive approximations in the Darboux problem for certain differential equations of the type $u_{x_1\cdots x_n}=f(x_1,\cdots,x_n,u,\cdots,u_{x_{l_1}\cdots x_{l_j}},\cdots)$. (English). Časopis pro pěstování matematiky, vol. 95 (1970), issue 2, pp. 178-195
MSC: 35A05 | MR 0450758 | Zbl 0191.11502 | DOI: 10.21136/CPM.1970.108350
References:
[1] W. Walter: Eindeutigkeitssätze für gewòhnliche, parabolische, und hyperbolische Differentialgleichungen. Math. Zeitschrift 74 (3) (1960), pp. 191 - 209. MR 0117427
[2] M. Kwapisz B. Palczewski, W. Pawelski: Sur ľunicité des solutions de certaines équations différentielles du type $u_{xyz} - f(x, y, z, u, u_x, u_y,u_z, u_{xy}, u_{xz}, u_{yz})$. Ann. Polon. Math. 11 (1961), pp. 75-106. MR 0136880
[3] B. Palczewski: On the uniqueness of solutions and the convergence of successive approximations in the Darboux problem under the conditions of the Krasnosielski and Krein type. Ann. Polon. Math. 14 (1964), pp. 183-190. MR 0161014 | Zbl 0132.07301
[4] J. S. W. Wong: On the convergence of successive approximations in the Darboux problem. Ann. Polon. Math. 17 (1966), pp. 329-336. MR 0188579 | Zbl 0144.13704
[5] E. R. van Kampen: Notes on systems of ordinary differеntial еquations. Amеrican Journal of Math. 63 (1941), pp. З71-З76.
[6] W. A. J. Luxemburg: On thе convеrgеncе of succеssivе approximàtions in thе thеory of ordinary diffеrеntial еquations II. Indag. Math. 20 (1958), pp. 540-546. MR 0124554
Partner of
EuDML logo