B. Rzepecki in [5] examined the Darboux problem for the hyperbolic equation on the quarter-plane x ≥ 0, y ≥ 0 via a fixed point theorem of B.N. Sadovskii [6]. The aim of this paper is to study the Picard problem for the hyperbolic equation using a method developed by A. Ambrosetti [1], K. Goebel and W. Rzymowski [2] and B. Rzepecki [5].
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1044,
author = {Antoni Sadowski},
title = {On the Picard problem for hyperbolic differential equations in Banach spaces},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {23},
year = {2003},
pages = {31-37},
zbl = {1053.35081},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1044}
}
Antoni Sadowski. On the Picard problem for hyperbolic differential equations in Banach spaces. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 23 (2003) pp. 31-37. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1044/
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[003] [4] B. Rzepecki, Measure of Non-Compactness and Krasnoselskii's Fixed Point Theorem, Bull. Acad. Polon. Sci., Sér. Sci. Math. 24 (1976), 861-866. | Zbl 0341.47039
[004] [5] B. Rzepecki, On the existence of solution of the Darboux problem for the hyperbolic partial differential equations in Banach Spaces, Rend. Sem. Mat. Univ. Padova 76 (1986). | Zbl 0656.35087
[005] [6] B.N. Sadovskii, Limit compact and condensing operators, Russian Math. Surveys 27 (1972), 86-144.