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Title: Asymptotics of Oscillating Solutions to Equations with Power Nonlinearities

Abstract

We present results on the existence of oscillating solutions of specific form (“quasiperiodic solutions) for a nonlinear differential equation with power nonlinearity. For oscillating solutions to third-order equations of this type, we obtain an asymptotics of extremums, which is expressed through the asymptotics of extremums of a “quasiperiodic” solution. These results clarify the asymptotic formulas for the modules of extremums of solutions obtained by the author earlier.

Authors:
 [1]
  1. M. V. Lomonosov Moscow State University (Russian Federation)
Publication Date:
OSTI Identifier:
22771293
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 230; Journal Issue: 5; Conference: International symposium on differential equations, Perm (Russian Federation), 17-18 May 2016; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ASYMPTOTIC SOLUTIONS; DIFFERENTIAL EQUATIONS; NONLINEAR PROBLEMS; PERIODICITY

Citation Formats

Astashova, I. V., E-mail: ast@diffiety.ac.ru. Asymptotics of Oscillating Solutions to Equations with Power Nonlinearities. United States: N. p., 2018. Web. doi:10.1007/S10958-018-3762-8.
Astashova, I. V., E-mail: ast@diffiety.ac.ru. Asymptotics of Oscillating Solutions to Equations with Power Nonlinearities. United States. doi:10.1007/S10958-018-3762-8.
Astashova, I. V., E-mail: ast@diffiety.ac.ru. Tue . "Asymptotics of Oscillating Solutions to Equations with Power Nonlinearities". United States. doi:10.1007/S10958-018-3762-8.
@article{osti_22771293,
title = {Asymptotics of Oscillating Solutions to Equations with Power Nonlinearities},
author = {Astashova, I. V., E-mail: ast@diffiety.ac.ru},
abstractNote = {We present results on the existence of oscillating solutions of specific form (“quasiperiodic solutions) for a nonlinear differential equation with power nonlinearity. For oscillating solutions to third-order equations of this type, we obtain an asymptotics of extremums, which is expressed through the asymptotics of extremums of a “quasiperiodic” solution. These results clarify the asymptotic formulas for the modules of extremums of solutions obtained by the author earlier.},
doi = {10.1007/S10958-018-3762-8},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 5,
volume = 230,
place = {United States},
year = {2018},
month = {5}
}