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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[1] O. A. Ivanov, “Ogranichennye resheniya kvazilineinykh sistem”, Vestnik LGU, 1985, no. 4, 99–100 | MR

[2] V. A. Pliss, Integralnye mnozhestva periodicheskikh sistem differentsialnykh uravnenii, Nauka, M., 1977, 304 pp. | MR | Zbl

[3] F. Khartman, Obyknovennye differentsialnye uravneniya, Mir, M., 1970, 720 pp. | MR | Zbl