Literature cited
H. Lewy, “Über das Anfangswertproblem für eine hyperbolisch nichtlinear Differential-gleichungen zweiter Ordnung mit zwei unabhängigen Veränderlichen,” Math. Ann.,98, 179–191 (1927).
R. Courant, Partial Differential Equations [Russian translation], Mir, Moscow (1964).
E. V. Shikin, “Equations of isometric imbeddings of two-dimensional manifolds of negative curvature in a three-dimensional Euclidean space,” Mat. Zametki,31, No. 4, 601–612 (1982).
P. Hartman, Ordinary Differential Equations, Wiley, New York (1964).
B. L. Rozhdestvenskii and N. N. Yanenko, Systems of Quasilinear Equations [in Russian], Nauka, Moscow (1978).
P. Hartman and A. Wintner, “On hyperbolic differential equations,” Am. J. Math.,74, 834–864 (1952).
A. Douglis, “Some existence theorems for hyperbolic systems of partial differential equations in two independent variables,” Commun. Pure. Appl. Math.,5, 119–154 (1952).
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Translated from Matematicheskie Zametki, Vol. 51, No. 6, pp. 80–90, June, 1992.
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Tynitskii, D.V. The Cauchy problem for a hyperbolic Monge-Ampère equation. Math Notes 51, 582–589 (1992). https://doi.org/10.1007/BF01263303
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DOI: https://doi.org/10.1007/BF01263303