Abstract
The paper presents some results on the existence and behaviour of some parameter classes of solutions for system of quasilinear differential equations. The behaviour of integral curves in neighbourhoods of an arbitrary curve is considered. The obtained results contain the answer to the question on stability as well as approximation of solutions whose existence is established. The errors of the approximation are defined by the functions that can be sufficiently small. The theory of qualitative analysis of differential equations and topological retraction method are used.
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References
J. Diblík, On asymptotic behaviour of solutions of certain classes of onlinary differential equations, Journal of Differential Equations 95 (1992), 203–217.
A. Omerspahić, Retraction method in the Qualitative Analysis of the Solutions of the Quasilinear Second Order Differential Equation, Proceedings of the First Conference on Applied Math. and Computation, Dubrovnik 1999, (2001).
B. Vrdoljak, Curvilinear "e;tubes"e; in the retraction method and the behaviour of solutions for the system of differential equations, Matematički Vesnik 4(17)(32) (1980), 381–392.
B. Vrdoljak, On parameter classes of solutions for system of linear differential equations, Glasnik Matematički 20(40)(1985) 61–69.
B. Vrdoljak, Existence and approximation of radial solutions of semilinear elliptic equations in an annulus, Glasnik Matematički 30(50) (1995), 243–259.
B. Vrdoljak, On behaviour and stability of system of linear differential equations, Proceedings of the 2nd Congress of Croatian Society of Mechanics, Supetar, 1997, 631–638.
B. Vrdoljak, On behaviour of solutions of system of linear differential equations, Mathematical Communications 2(1997) 47–57.
B. Vrdoljak and A. Omerspahić, Qualitative analysis of some solutions of quasilinear system of differential equations, Proceedings of the Second Conference on Applied Mathematics and Scientific Computing, Edited by Z. Drmaè et al., Kluver Academic/Plenum Publishers, New York (2003), 323–332.
T. Wažewski, Sur un principe topologique de l'examen de l'allure asymptotique des integrales des equations differentielles ordinaires, Ann. Soc. Polon. Math. 20 (1947), 279–313.
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Omerspahić, A., Vrdoljak, B. (2005). On Parameter Classes of Solutions for System of Quasilinear Differential Equations. In: Drmač, Z., Marušić, M., Tutek, Z. (eds) Proceedings of the Conference on Applied Mathematics and Scientific Computing. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3197-1_19
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DOI: https://doi.org/10.1007/1-4020-3197-1_19
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3196-0
Online ISBN: 978-1-4020-3197-7
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