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The convergence of successive approximations for boundary value problems of hyperbolic equations in the Banach space. (English) Zbl 0209.12302

MSC:
35A35 Theoretical approximation in context of PDEs
35L50 Initial-boundary value problems for first-order hyperbolic systems
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References:
[1] Borůvka O.: Diferenciálne rovnice. Bratislava, 1961.
[2] Edelstein M.: On fixed and periodic points under contractive mappings. J. London Math. Soc. 37 (1962), 74-79. · Zbl 0113.16503 · doi:10.1112/jlms/s1-37.1.74
[3] Luxemburg W. A. J.: On the couvergence of successive approximations in the theory of ordinary differential equations II. Indag. Math. 20 (1958), 540 546. · Zbl 0084.07703
[4] Ďurikovič V.: On the uniqueness of solutions and on the convergence of successive approximations for certain initial problems of equations of higher orders. Mat. časop. 20 (1970), 212-224. · Zbl 0206.11002
[5] Ďurikovič V.: The existence and uniqueness of solutions of boundary value problems in non-linear partial differential equations of the hyperbolic type. Acta Fac. Rer. Mat. Univ. Comen. - Math. XXIII, (1970), 41-51. · Zbl 0212.12902
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