A new approach to the existence of quasiperiodic solutions for a class of semilinear Duffing-type equations with time-periodic parameters

Xiaoming Wang, Lixia Wang, Hainv Tan
2016 Boundary Value Problems  
Let q(t) be a continuous 2π -periodic function with 1 2π 2π 0 q(t) dt > 0. We propose a new approach to establish the existence of Aubry-Mather sets and quasi-periodic solutions for the following time-periodic parameters semilinear Duffing-type equation: ) is a continuous function, 2π -periodic in the first argument and continuously differentiable in the second one. Under some assumptions on the functions q and f , we prove that there are infinitely many generalized quasi-periodic solutions via
more » ... a version of the Aubry-Mather theorem given by Pei. Especially, an advantage of our approach is that it does not require any high smoothness assumptions on the functions q(t) and f (t, x).
doi:10.1186/s13661-016-0640-5 fatcat:3gaexxegsjg7xlt755uxcxceau