Boundedness of solutions for semilinear Duffing’s equation with asymmetric nonlinear term

摘要

In this paper we study the following second-order periodic system: x ″ + V ′ ( x ) + p ( x ) f ( t ) = 0 , where V ( x ) has a singularity. Under some assumptions on the V ( x ) , p ( x ) and f ( t ) , by Ortega’s small twist theorem, we obtain the existence of quasi-periodic solutions and boundedness of all the solutions.