We prove the existence of a pair of positive T -periodic solutionsas well as the existence of positive subharmonic solutions of anyorder and the presence of chaotic-like dynamics for the scalarsecond order ODEu +aλ,μ(t)g(u) = 0,where g(x) is a positive function on R+, superlinear at zero andsublinear at infinity, and aλ,μ(t) is a T -periodic and sign indefiniteweight of the form λa+(t)−μa−(t), with λ,μ > 0 and large.
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