Existence and continuation of periodic solutions of Newtonian systems
J. Fura, A. Ratajczak & S. Rybicki
TL;DR
This paper investigates the existence and continuation of periodic solutions in autonomous Newtonian systems using advanced topological degree theory, highlighting limitations of traditional methods like Leray-Schauder degree.
Contribution
It introduces an application of infinite-dimensional SO(2)-equivariant degree theory to analyze periodic solutions, overcoming the limitations of Leray-Schauder degree.
Findings
Established existence results for periodic solutions.
Demonstrated the continuation of solutions under certain conditions.
Showed the inapplicability of Leray-Schauder degree in this context.
Abstract
In this article we study the existence and the continuation of periodic solutions of autonomous Newtonian systems. To prove the results we apply the infinite-dimensional version of the degree for SO(2)-equivariant gradient operators. Using the results due to Rabier we show that the Leray-Schauder degree is not applicable in the proofs of our theorems, because it vanishes.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Nonlinear Differential Equations Analysis · Advanced Mathematical Modeling in Engineering