Lagrange stability for a class of impulsive Duffing equation with low regularity

Abstract

We discuss the Lagrange stability for a class of impulsive Duffing equation with time-dependent polynomial potentials. More precisely, we prove that under suitable impulses, all the solutions of the impulsive Duffing equation (with low regularity in time) are bounded for all time and that there are many (positive Lebesgue measure) quasi-periodic solutions clustering at infinity.

Keywords

• boundedness
• quasi-periodic solution
• moser's twist theorem
• impulsive duffing equation