Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 120, pp. 1-11.

Title: Linking method for periodic non-autonomous fourth-order
       differential equations with superquadratic potentials

Authors: Chengyue Li  (Minzu Univ., Beijing, China)
         Changhua Shi (Minzu Univ., Beijing, China)

Abstract:
 By means of the Schechter's Linking method, we study the
 existence of 2T-periodic solutions of the non-autonomous
 fourth-order ordinary differential equation
 $$
 u''''-Au''-Bu-V_u(t,u)=0
 $$
 where $A>0$, $B>0$, $V(t,u)\in \mathbb{C}^1(\mathbb{R}\times\mathbb{R},
 \mathbb{R})$ is 2T-periodic in t and satisfies either
 $0<\theta V(t,u) \leq u V_u(t,u)$ with  $\theta>2$, or
 $u V_u(t,u)-2V(t,u)\geq d_3|u|^r$ with $r\geq 1$.

Submitted June 18, 2009. Published September 27, 2009.
Math Subject Classifications: 58E05, 34C37, 70H05.
Key Words: Periodic solutions; fourth-order differential equations;
           linking theorem; critical points.