Theorem on the existence of an invariant section over $\mathbb{R}^m$ for the indefinite monotone system in $\mathbb{R}^m × \mathbb{R}^n$ - Lagoda, V. A.; Parasyuk, I. O. (Ukrains’kyi Matematychnyi Zhurnal, 2013)
We consider a nonlinear system on the direct product $\mathbb{R}^m × \mathbb{R}^n$. For this system, under the conditions of indefinite coercivityand indefinite monotonicity, we establish the existence of a bounded Lipschitzian invariant section over $\mathbb{R}^m$.