Boundedness of solutions for asymmetric Duffing equations

摘要

In this paper, we are concerned with the boundedness of all the solutions and the existence of quasiperiodic solutions for some Duffing equations x¨+g(x)=e(t), where e(t) is of period 1, and g : R → R possesses the characters: g(x) is superlinear when x ⩾ d0, d0 is a positive constant and g(x) is semilinear when x ⩽ 0.