Activities per year
Abstract
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 phasespace 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 phasespace 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 pLaplacian and the prescribed curvature equation.
Original language  English 

Pages (fromto)  243257 
Number of pages  15 
Journal  Monatshefte für Mathematik 
Volume  199 
Issue number  2 
DOIs  
Publication status  Published  12 Jan 2022 
Keywords
 nonautonomous systems
 generalised Liénard equation
 prescribed curvature operator
 relativistic acceleration
 pLaplacian
 positively invariant sets
 Brouwer fixed point
 periodic orbits
 Generalized Liénard equations
 φLaplacian
 Relativistic acceleration
 Brouwer fixed point theorem
 Nonautonomous systems
 Prescribed curvature operator
 Positively invariant sets
Fingerprint
Dive into the research topics of 'Existence of harmonic solutions for some generalisation of the nonautonomous Liénard equations'. Together they form a unique fingerprint.Activities
 1 Participation in workshop, seminar, course

Two days on qualitative theory of differential equations
Timoteo Carletti (Speaker)
30 Sep 2022 → 1 Oct 2022Activity: Participating in or organising an event types › Participation in workshop, seminar, course