Geodesic
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 $u_{x_1\cdots x_n}=f(x_1,\cdots,x_n,u,\cdots,u_{x_{l_1}\cdots x_{l_j}},\cdots)$
Časopis pro pěstování matematiky, Tome 95 (1970) no. 2, pp. 178-195

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DOI MR   Zbl

DOI : 10.21136/CPM.1970.108350
Classification : 35A05 
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 $u_{x_1\cdots x_n}=f(x_1,\cdots,x_n,u,\cdots,u_{x_{l_1}\cdots x_{l_j}},\cdots)$. Časopis pro pěstování matematiky, Tome 95 (1970) no. 2, pp. 178-195. doi: 10.21136/CPM.1970.108350
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     title = {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 $u_{x_1\cdots x_n}=f(x_1,\cdots,x_n,u,\cdots,u_{x_{l_1}\cdots x_{l_j}},\cdots)$},
     journal = {\v{C}asopis pro p\v{e}stov\'an{\'\i} matematiky},
     pages = {178--195},
     year = {1970},
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[1] W. Walter: Eindeutigkeitssätze für gewòhnliche, parabolische, und hyperbolische Differentialgleichungen. Math. Zeitschrift 74 (3) (1960), pp. 191 - 209. | MR

[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

[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 | Zbl

[4] J. S. W. Wong: On the convergence of successive approximations in the Darboux problem. Ann. Polon. Math. 17 (1966), pp. 329-336. | MR | Zbl

[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

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