Periodic solutions of nonlocal semilinear fourth-order differential equations (Q549939)

The authors study the existence of periodic solutions for two classes of nonlocal fourth-order nonautonomous differential equations of the type \[ u^{iv}-pu''\pm a(x)u+u(x)\int_0^L f(x,y)u^2(y)\,dy=0. \] Correspondingly, they have two multiplicity results, which are proved by a clever use of standard variational methods.