Existence of harmonic solutions for some generalisation of the non-autonomous Liénard equations

Autor:	Timoteo Carletti, Gabriele Villari, Fabio Zanolin
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	prescribed curvature operator generalised Liénard equation positively invariant sets φ-Laplacian General Mathematics Non-autonomous systems p-Laplacian Generalized Liénard equations Brouwer fixed point relativistic acceleration Brouwer fixed point theorem periodic orbits
Zdroj:	Carletti, T, Villari, G & Zanolin, F 2022, ' Existence of harmonic solutions for some generalisation of the non-autonomous Liénard equations ', Monatshefte für Mathematik, vol. 199, no. 2, pp. 243-257 . https://doi.org/10.1007/s00605-021-01652-3
DOI:	10.1007/s00605-021-01652-3
Popis:	We study the problem of existence of harmonic solutions for some generalisations of the periodically perturbed Liénard equation, where the damping function depends both on the position and the velocity. In the associated phase-space this corresponds to a term of the form f(x, y) instead of the standard dependence on x alone. We introduce suitable autonomous systems to control the orbits behaviour, allowing thus to construct invariant regions in the extended phase-space and to conclude about the existence of the harmonic solution, by invoking the Brouwer fixed point Theorem applied to the Poincaré map. Applications are given to the case of the p-Laplacian and the prescribed curvature equation.
Databáze:	OpenAIRE
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