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 ) ∈ L p ( R / T Z ) for which the periodic linear beam equation u ( 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.