Non-degeneracy and uniqueness of periodic solutions for some superlinear beam equations

In this work we will use some Sobolev constants to explicitly characterize a class of potentials q(t)∈Lp(R/TZ)q(t)∈Lp(R/TZ) for which the periodic linear beam equation u(4)=q(t)uu(4)=q(t)u is non-degenerate. As an application, we will obtain the uniqueness of periodic solutions of a certain class of superlinear beam equations.