01233nas a2200133   4500008004100000245007600041210006900117300001200186490000700198520080200205100002301007700002301030856004601053       2018                        eng d00aPositive subharmonic solutions to nonlinear ODEs with indefinite weight0 aPositive subharmonic solutions to nonlinear ODEs with indefinite  a17500210 v203 a<p>We prove that the superlinear indefinite equation u″ + a(t)up = 0, where p &gt; 1 and a(t) is a T-periodic sign-changing function satisfying the (sharp) mean value condition ∫0Ta(t)dt &lt; 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) 467–477]. The proof, which applies to a larger class of indefinite equations, combines coincidence degree theory (yielding a positive harmonic solution) with the Poincaré–Birkhoff fixed point theorem (giving subharmonic solutions oscillating around it).</p>1 aBoscaggin, Alberto1 aFeltrin, Guglielmo  uhttps://doi.org/10.1142/S0219199717500213