Infinitely Many Solutions for a Floquet-Type BVP with Superlinearity Indefinite in Sign

By the application of a technique developed by G. J. Butler we find infinitely many solutions of the BVP ¨xqq t.g x. s0 x v.,˙x v..sL x 0.,˙x 0.., where q :w0, vxªR is allowed to change sign, g : RªR is superlinear and g x.x)0 for all x/0, and L : R2ªR2is a continuous, positively homogeneous, and nondegenerate map. At first we apply the main result to obtain solutions with a prescribed large number of zeros when L is the rotation of a fixed angle l; second, we find infinitely many subharmonic solutions of any order and, again, solutions with a prescribed large number of zeros for the periodic problem associated to the equation ¨xqc˙xqq t.g x.s0, with q and g as above and cgR. Q