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

• Date: 2013
• Main Authors: Lagoda, V. A., Parasyuk, I. O., Лагода, В. А., Парасюк, І. О.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2013
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2407
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 $\mathbb{R}^m$.