Bounded solutions: Differential vs difference equations

Abstract

We compare some recent results on bounded solutions (over $Z$) of nonlinear difference equations and systems to corresponding ones for nonlinear differential equations. Bounded input-bounded output problems, lower and upper solutions, Landesman-Lazer conditions and guiding functions techniques are considered.

Keywords

• Difference equations
• bounded solutions
• lower-upper solutions
• Landesman-Lazer conditions
• guiding functions