We prove that the superlinear indefinite equation u" + a(t)up = 0, where p \> 1 and a(t) is a T-periodic sign-changing function satisfying the (sharp) mean value condition ∫0Ta(t)dt \< 0, has positive subharmonic solutions of order k for any large integer k, thus providing a further contribution to a problem raised by Butler in its pioneering paper [Rapid oscillation, nonextendability, and the existence of periodic solutions to second order nonlinear ordinary differential equations, J. Differential Equations 22 (1976) 467{\textendash}477]. The proof, which applies to a larger class of indefinite equations, combines coincidence degree theory (yielding a positive harmonic solution) with the Poincar{\'e}{\textendash}Birkhoff fixed point theorem (giving subharmonic solutions oscillating around it).

}, doi = {10.1142/S0219199717500213}, url = {https://doi.org/10.1142/S0219199717500213}, author = {Alberto Boscaggin and Guglielmo Feltrin} }