2019
Том 71
№ 11

All Issues

Mawhin J.

Articles: 2
Article (English)

Variations on some finite-dimensional fixed-point theorems

Mawhin J.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 2. - pp. 266-272

We give rather elementary topological proofs of some generalizations of fixed-point theorems in $\mathbb{R}^n$ due to Pireddu-Zanolin and Zgliczynski, which are useful in various questions related to ordinary differential equations.

Article (English)

Resonance and nonlinearity: A survey

Mawhin J.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 2. - pp. 190–205

This paper surveys recent results about nonresonant and resonant periodically forced nonlinear oscillators. This includes the existence of periodic, unbounded or bounded solutions for bounded nonlinear perturbations of linear and piecewise-linear oscillators, as well as of some classes of planar Hamiltonian systems.