Geodesic
On minima of functionals and implicit differential equations
Vestnik rossijskih universitetov. Matematika, Tome 22 (2017) no. 6, pp. 1298-1303

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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
Mots-clés : implicit ODE. 
S. E. Zhukovskiy. On minima of functionals and implicit differential equations. Vestnik rossijskih universitetov. Matematika, Tome 22 (2017) no. 6, pp. 1298-1303. http://geodesic.mathdoc.fr/item/VTAMU_2017_22_6_a10/
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[1] A. V. Arutyunov, “Caristi's condition and existence of a minimum of a lower bounded function in a metric space. Applications to the theory of coincidence points”, Optimal control, Collected papers. In commemoration of the 105th anniversary of Academician Lev Semenovich Pontryagin, Proc. Steklov Inst. Math., 291, 2015, 24–37 | DOI | MR | Zbl

[2] A. N. Kolmogorov, S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, Nauka, Moscow, 1976 (In Russian) | MR

[3] P. P. Zabreiko, A. I. Koshelev, M. A. Krasnosel’skii, et al., Integral Equations, Nauka, Moscow, 1968 (In Russian)

[4] J. Warga, Optimal Control of Differential and Functional Equations, Academic Press, New York, 1972 | MR | Zbl