On the perturbability of the asymptotic manifold of a perturbed system of differential equations

Ladas, G.; Lakshmikantham, V.; Leela, S.

doi:10.1090/S0002-9939-1971-0274888-3

On the perturbability of the asymptotic manifold of a perturbed system of differential equations
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by G. Ladas, V. Lakshmikantham and S. Leela PDF

Proc. Amer. Math. Soc. 27 (1971), 65-71 Request permission

Abstract:

We investigate the asymptotic relationship between the solutions of a linear differential system and its perturbed system. Our results depend upon a known result of F. Brauer on asymptotic equilibrium. We also study the asymptotic manifold of solutions of the nonlinear system generated by the solutions of the corresponding linear system.

References

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T. G. Hallam and J. W. Heidel, The asymptotic manifolds of a perturbed linear system of differential equations, Trans. Amer. Math. Soc. 149 (1970), 233–241. MR 257486, DOI 10.1090/S0002-9947-1970-0257486-0

Differential and integral inequalities, theory and applications

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