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We investigate the existence of positive solutions for a class of Minkowski-curvature equations with indefinite weight and nonlinear term having superlinear growth at zero and super-exponential growth at infinity. As an example, for the equation ( u ′ 1 − (u ′) 2 ) ′ + a (t) (e u p − 1) = 0 , where p > 1 and a (t) is a sign-changing function satisfying the mean-value condition ∫ 0 T a (t) d t < 0 , we prove the existence of a positive solution for both periodic and Neumann boundary conditions. The proof relies on a topological degree technique. [ABSTRACT FROM AUTHOR]

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]