TY - JOUR AU - V. A. Lagoda AU - I. O. Parasyuk PY - 2013/01/25 Y2 - 2024/03/29 TI - Theorem on the existence of an invariant section over $\mathbb{R}^m$ for the indefinite monotone system in $\mathbb{R}^m \times \mathbb{R}^n$ JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 65 IS - 1 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2407 AB - We consider a nonlinear system on the direct product $\mathbb{R}^m \times \mathbb{R}^n$. For this system, under the conditions of indefinite coercivityand indefinite monotonicity, we establish the existence of a bounded Lipschitzian invariant section over $\mathbb{R}^m$. ER -