On a kind of symmetric weakly non-linear ordinary differential systems

0457324 - MÚ 2017 RIV NL eng J - Journal Article
Fečkan, M. - Rontó, András - Dilna, N.
On a kind of symmetric weakly non-linear ordinary differential systems.
Bulletin des Sciences Mathématiques. Roč. 140, č. 2 (2016), s. 188-230. ISSN 0007-4497. E-ISSN 1952-4773
Institutional support: RVO:67985840
Keywords : symmetric solution * symmetry * periodic solution
Subject RIV: BA - General Mathematics
Impact factor: 0.750, year: 2016
http://www.sciencedirect.com/science/article/pii/S0007449715000895

For a class of weakly non-linear ordinary differential equations, the existence of a unique symmetric solution is established and its stability is studied. The symmetry of a solution is understood in the sense of a certain linear functional equality which includes, in particular, the cases of periodic, anti-periodic, even, and odd solutions. Efficient stability conditions in terms of logarithmic norms and spectral stability conditions are obtained. The theory is illustrated by examples.
Permanent Link: http://hdl.handle.net/11104/0257715