Geodesic
Tychonoff--Schauder Theorem and the existence of bounded solutions of quasi-linear hyperbolic systems of differential equations
Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 12, Tome 352 (2008), pp. 114-119

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Tychonoff–Schauder fixed-point theorem is applied to prove the existence of bounded solutions of systems of ordinary differential equations which are $C^0$-close to linear hyperbolic systems. Bibl. – 3 titles. 
@article{ZNSL_2008_352_a3,
     author = {O. A. Ivanov},
     title = {Tychonoff--Schauder {Theorem} and the existence of bounded solutions of quasi-linear hyperbolic systems of differential equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {114--119},
     publisher = {mathdoc},
     volume = {352},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_352_a3/}
}
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O. A. Ivanov. Tychonoff--Schauder Theorem and the existence of bounded solutions of quasi-linear hyperbolic systems of differential equations. Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 12, Tome 352 (2008), pp. 114-119. http://geodesic.mathdoc.fr/item/ZNSL_2008_352_a3/