On periodic solutions of the system (dx(t)/dtdt)+b(t)V1'(x(t))+V2'(x(t)))=0 where b(·) changes sign and V1, V2 have different superquadratic growths

In this paper a nonautonomous second order system of the type (dx(t)/dtdt)+b(t)(V1'(x(t))+V2'(x(t)))=0, where b(·) is a real T-periodic function which changes sign and V1, V2 have different superquadratic growths, is considered. An existence result is stated in case that b(·) goes to zero with a sufficiently high order α at its zeroes and V1 is homogeneous with degree β>2 outside of a sphere, where β varies in a suitable set depending on α. The techniques of the proof are based on the use of a truncation argument and some Morse index estimates for critical points of Mountain Pass type. (author)