Averaging methods for nonlinear systems with a small parameter via reduction and topological degree

DOI10.1016/j.nonrwa.2018.07.019zbMath1460.34047OpenAlexW2885348550WikidataQ129447886 ScholiaQ129447886MaRDI QIDQ1729175

Qihuai Liu, Luocheng Cai

Publication date: 27 February 2019

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2018.07.019

zbMATH Keywords

periodic solutiontopological degreeLyapunov-Schmidt reductionaveraging method

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Averaging method for ordinary differential equations (34C29) Applications of operator theory to differential and integral equations (47N20) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Nonautonomous smooth dynamical systems (37C60)

Related Items (2)

Periodic solutions of nonlinear differential systems by the method of averaging. ⋮ Unnamed Item

Cites Work

• Improving the averaging theory for computing periodic solutions of the differential equations
• New results on averaging theory and applications
• Periodic averaging principle in quantum calculus
• Lyapunov-Schmidt reductions and Melnikov integrals for bifurcation of periodic solutions in coupled oscillators
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• Periodic solutions of the elliptic isosceles restricted three-body problem with collision by the averaging method
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• Averaging theory for discontinuous piecewise differential systems
• Periodic solutions of nonlinear periodic differential systems with a small parameter
• Modulated amplitude waves with nonzero phases in Bose-Einstein condensates
• Higher order averaging theory for finding periodic solutions via Brouwer degree
• Regularization of kepler's problem and the averaging method on a manifold
• Averaging methods in nonlinear dynamical systems
• Unnamed Item

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