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[formula]where q:[0,ω]→R is allowed to change sign, g:R→R is superlinear and g(x)x0 for all x≠0, and Λ:R2→R2 is 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 Λ is the rotation of a fixed angle λ; 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 ẍ+cẋ+q(t)g(x)=0, with q and g as above and c∈R. © 2000 Academic Press.