Positive subharmonic solutions to nonlinear ODEs with indefinite weight.

We prove that the superlinear indefinite equation where and is a -periodic sign-changing function satisfying the (sharp) mean value condition , has positive subharmonic solutions of order for any large integer , 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). [ABSTRACT FROM AUTHOR]