Semicontinuous solutions of systems of functional equations

Herzog, Gerd

facul_02; 02

Date: 25. 02. 2002
Abstract:
We use the method of upper and lower solutions to prove the existence
of upper and lower semicontinuous solutions of functional equations of
the form $F(\omega,u(\omega),u(g_1(\omega)),\dots,u(g_m(\omega)))=0$ in $\mathbb{R}^n$ under mono-
tonicity and quasimonotonicity assumptions on $F$, and for $\omega$ from a
metrizable topological space.

Primary MSC: 43A40 Character groups and dual objects
Secondary MSC: 39B52 Equations for functions with more general domains and/or ranges, 39B72 Inequalities involving unknown functions