Electron. J. Diff. Equ., Vol. 2009(2009), No. 120, pp. 1-11.

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

Chengyue Li, Changhua Shi

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.

Show me the PDF file (252 KB), TEX file, and other files for this article.

Chengyue Li
Department of Mathematics, Minzu University of China
Beijing 100081, China.
email: cunlcy@163.com
Changhua Shi
Department of Mathematics, Minzu University of China
Beijing 100081, China.
email: shichanghua88888@163.com

Return to the EJDE web page