Periodic Duffing equations with delay

Abstract

Assuming a priori bounds on the mean of a $T$-periodic function $p$, we show that the Duffing equation $$ x''(t) +cx'(t) +g(t-au,x(t-au), x'(t-au)) =p(t), $$ with delay $au$, admits a $T$-periodic solution.

Keywords

• Duffing equations
• periodic solutions
• delay equations
• a priori bounds
• contraction principle.