Premium
Unbounded Solutions in Non‐Smooth Dynamical Systems at Resonance
Author(s) -
Kunze M.
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19980781562
Subject(s) - resonance (particle physics) , dynamical systems theory , ode , forcing (mathematics) , ordinary differential equation , nonlinear system , phase plane , mathematical analysis , fourier transform , plane (geometry) , fourier series , mathematics , complex plane , phase (matter) , differential inclusion , differential equation , physics , geometry , quantum mechanics
We consider periodically forced non‐smooth dynamical systems at resonance, described by differential inclusions, and we show that analogously to the case of ODEs all solutions are unbounded in the ( x )‐phase plane, if the first Fourier coefficient of the forcing is large compared to a certain quantity related to the nonlinearity.