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.