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A non-linear Goursat problem for a high order polyvibrating equation

Published online by Cambridge University Press:  14 November 2011

Andrzej Borzymowski
Andrzej Borzymowski
Affiliation:
Institute of Mathematics, Warsaw University of Technology, PI. Jedności Robotniczej 1, Warsaw, Poland
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Synopsis

This paper proves the existence of a solution of a non-linear Goursat problem for a partial differential equation of order 2p (p ≧ 2) with the boundary conditions given on 2p curves emanating from a common point. The problem is reduced to a system of integro-differential-functional equations and then Schauder's fixed point theorem is applied.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 102 , Issue 1-2 , 1986 , pp. 159 - 172
Copyright
Copyright © Royal Society of Edinburgh 1986

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References

1Bielecki, A. and Kisyński, J.. Sur le problème de E. Goursat relatif a l'équation ə 2z/əx əy = f(x, y). Ann. Univ. Mariae Curie-Skłodowska 10A (1956), 99–126.Google Scholar
2Borzymowski, A.. A non-linear Goursat problem for a 4th order polyvibrating equation. Proc. Roy. Soc. Edinburgh Sect. A 92 (1982), 153–164.CrossRefGoogle Scholar
3Borzymowski, A.. Concerning a Goursat problem for some partial differential equation of order 2p. Demonstratio Math. 18 (1985), 253–277.Google Scholar
4Mangeron, D.. Problèmes à la frontière concernant les équations polyvibrantes. C.R. Acad. Sci. Paris Sér. A 266 (1968), 870–73; 976–79; 1103–06; 1121–24.Google Scholar
5Oğuztöreli, M. N.. Sur le problème de Goursat pour une équation de Mangeron d'ordre supéneur I, II. Bull. Acad. Roy. Belg. Cl. Sci. 58 (1972), 464–71; 577–82.Google Scholar
6Oğuztöreli, M. N.. Sur un problème mixte concernant une equation polyvibrante d'ordre supérieur de Mangeron. Bull. Acad. Roy. Belg. Cl. Sci. 58 (1972), 740–46.Google Scholar