Theorem on the existence of an invariant section over R^m for the indefinite monotone system in R^m × R^n - Lagoda, V. A.; Parasyuk, I. O. (Ukrains’kyi Matematychnyi Zhurnal, 2013)
We consider a nonlinear system on the direct product R^m × 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 R^m.