2019
Том 71
№ 8

All Issues

Lagoda V. A.

Articles: 2
Article (Ukrainian)

Theorem on the existence of an invariant section over $\mathbb{R}^m$ for the indefinite monotone system in $\mathbb{R}^m \times \mathbb{R}^n$

Lagoda V. A., Parasyuk I. O.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 1. - pp. 103-118

We consider a nonlinear system on the direct product $\mathbb{R}^m \times \mathbb{R}^n$. For this system, under the conditions of indefinite coercivity and indefinite monotonicity, we establish the existence of a bounded Lipschitzian invariant section over $\mathbb{R}^m$.

Article (Ukrainian)

Lipschitzian invariant tori of indefinite monotone system

Lagoda V. A., Parasyuk I. O., Samoilenko A. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 3. - pp. 363-383

We consider a nonlinear system in the direct product of a torus and a Euclidean space. For this system, under the conditions of indefinite coercivity and indefinite monotonicity, we establish the existence of a Lipschitzian invariant section.