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On minima of functionals and implicit differential equations

Annotation

The stability of Caristi-like conditions under small Lipschitz perturbations is proved for functionals on metric spaces. The result obtained is used for the investigation of implicit differential equation. Sufficient conditions for solvability of Cauchy problem for implicit ordinary differential equations are obtained.

Keywords

Caristi-like conditions; minimum; implicit ODE

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DOI

10.20310/1810-0198-2017-22-6-1298-1303

UDC

517.922

Pages

1298-1303

References

1 . Arutyunov A.V. Caristi’s condition and existence of a minimum of a lower bounded function in a metric space. Applications to the theory of coincidence points // Proc. Steklov Inst. Math. 2015. V. 291. P. 30–44. 2 . Kolmogorov A.N., Fomin S.V. Elements of the Theory of Functions and Functional Analysis. M.: Nauka, 1976. 3 . Zabreiko P.P., Koshelev A.I., Krasnosel’skii M.A., et al. Integral Equations. M.: Nauka, 1968. 4 . Warga J. Optimal Control of Differential and Functional Equations. N.Y.: Academic Press, 1972.

Received

2017-08-13

Section of issue

Mathematics

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