Abstract :
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
