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Existence of convergent solutions to quasi-linear systems and asymptotic equivalence. (English) Zbl 0245.34029


MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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References:

[1] Avramescu, C.: Sur l’existence des solutions convergentes d’équations différentielles non linéaires. Ann. mat. Pura appl. 4, 147-168 (1969) · Zbl 0196.10701
[2] Hallam, T. G.; Heidel, J. W.: The asymptotic manifolds of a perturbed linear system of differential equations. Trans. amer. Math. soc. 149, 233-241 (1970) · Zbl 0186.41502
[3] Fennel, R. E.; Proctor, T. G.: On asymptotic behavior of perturbed nonlinear systems. Proc. amer. Math. soc. 31, 499-504 (1972) · Zbl 0211.40101
[4] Kartsatos, A. G.: On the relationship between a nonlinear system and its non-linear perturbation. J. differential equations 11, 582-591 (1972) · Zbl 0226.34031
[5] Kartsatos, A. G.: Convergence in perturbed nonlinear systems. Tôhoku math. J. 24 (1972) · Zbl 0231.34033
[6] Ladas, G.; Lakshmikantham, V.; Leela, S.: On the perturbability of the asymptotic manifold of a perturbed system of differential equations. Proc. amer. Math. soc. 27, 65-71 (1971) · Zbl 0213.36502
[7] Onuchic, N.: Asymptotic equivalence between two systems of ordinary differential equations. Portugal math. 30, 97-105 (1971) · Zbl 0226.34032
[8] Staikos, V.: On the asymptotic relationship at infinity between the solutions of two differential systems. Bull. soc. Math. grèce 13, 1-11 (1972) · Zbl 0273.34023
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