| Abstract: |
| We prove the existence of infinitely many subharmonic solutions for a second-order
scalar nonlinear ODE of the form $u`` + g(t,u)=0,$ which can be considered
as a periodic perturbation of an autonomous Duffing-type equation
$u`` + g(u)=0$ with $g$ having a singularity at the origin.
We investigate two main different models, considering the case of $g(u)$
having superlinear or sublinear growth at infinity. The presence of positive
bounded solutions exhibiting complex dynamics is discussed as well. |
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