01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
19.02.1982
E-mail:
,
Keywords:
method of averaging, Levinson theorem, systems with oscillatory decreasing coefficients, Van-der-Pol equation, linear difference equations, asymptotic integration.
Subject:
Systems with oscillatory decreasing coefficients; singularly perturbed systems; normal & quasinormal forms methods; asymptotic methods in differential equations theory.
Main publications:
Nesterov P.N., “Metod usredneniya v zadache asimptoticheskogo integrirovaniya sistem s kolebatelno ubyvayuschimi koeffitsientami”, Differentsialnye uravneniya, 43:6 (2007), 731-742
Nesterov P., “Method of averaging for systems with main part vanishing at infinity”, Mathematische Nachrichten, 284:11-12 (2011), 1496-1514
Nesterov P., “Appearance of new parametric resonances in time-dependent harmonic oscillator”, Results in Mathematics, 64:3-4 (2013), 229-251
Nesterov P., “On some extension of center manifold method to functional differential equations with oscillatory decreasing coefficients and variable delays”, Journal of Dynamics and Differential Equations, 30:4 (2018), 1797-1816
Nesterov P., “Asymptotic summation of perturbed linear difference systems in critical case”, Journal of Difference Equations and Applications, 25:8 (2019), 1173-1199
P. N. Nesterov, J. I. Stavroulakis, “Triple equivalence of the oscillatory behavior for scalar delay differential equations”, TMF, 220:1 (2024), 113–136; Theoret. and Math. Phys., 220:1 (2024), 1157–1177
2017
2.
P. N. Nesterov, “Asymptotic integration of certain differential equations in Banach space”, Model. Anal. Inform. Sist., 24:5 (2017), 596–614
3.
P. N. Nesterov, “Asymptotics for solutions of harmonic oscillator with integral perturbation”, Model. Anal. Inform. Sist., 24:1 (2017), 64–81
2016
4.
P. N. Nesterov, “Asymptotic integration of a certain second-order linear delay differential equation”, Model. Anal. Inform. Sist., 23:5 (2016), 635–656
5.
P. N. Nesterov, “Erratum to: Center manifold method in the asymptotic integration problem for functional differential equations with oscillatory decreasing coefficients. II”, Model. Anal. Inform. Sist., 23:1 (2016), 86–88
2014
6.
P. N. Nesterov, “Center manifold method in the asymptotic integration problem for functional differential equations with oscillatory decreasing coeffcients. II”, Model. Anal. Inform. Sist., 21:5 (2014), 5–37
P. N. Nesterov, “Center Manifold Method in the Asymptotic Integration Problem for Functional Differential Equations with Oscillatory Decreasing Coefficients. I”, Model. Anal. Inform. Sist., 21:3 (2014), 5–34
P. N. Nesterov, “Parametric Resonance in a Time-Dependent Harmonic Oscillator”, Model. Anal. Inform. Sist., 20:3 (2013), 5–28
2011
10.
P. N. Nesterov, “On asymptotics for critical solutions of systems of differential equations with oscillatory decreasing coefficients”, Model. Anal. Inform. Sist., 18:3 (2011), 21–41
P. N. Nesterov, “Time scales and the asymptotics for the solutions of discrete adiabatic oscillators”, Model. Anal. Inform. Sist., 18:1 (2011), 5–27
2009
12.
A. V. Dymov, P. N. Nesterov, “Mathematical justification of one numerical experiment”, Model. Anal. Inform. Sist., 16:4 (2009), 56–76
2008
13.
P. N. Nesterov, “On the stability of solutions of some equations from the class of adiabatic oscillators”, Model. Anal. Inform. Sist., 15:2 (2008), 10–17
P. N. Nesterov, “The asymptotic representation of solutions of difference equations systems and the averaging method”, Model. Anal. Inform. Sist., 14:2 (2007), 63–67
P. N. Nesterov, “Construction of the Asymptotics of the Solutions
of the One-Dimensional Schrödinger Equation
with Rapidly Oscillating Potential”, Mat. Zametki, 80:2 (2006), 240–250; Math. Notes, 80:2 (2006), 233–243
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