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

• Main Authors: Chengyue Li, Changhua Shi
• Format: Article
• Language: English
• Published: Texas State University 2009-09-01
• Series: Electronic Journal of Differential Equations
• Subjects: Periodic solutions; fourth-order differential equations; linking theorem; critical points
• Online Access: http://ejde.math.txstate.edu/Volumes/2009/120/abstr.html

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 $A>0$, $B>0$, $V(t,u)in mathbb{C}^1(mathbb{R}imesmathbb{R}, mathbb{R})$ is 2T-periodic in t and satisfies either $0<heta V(t,u) leq u V_u(t,u)$ with $heta>2$, or $u V_u(t,u)-2V(t,u)geq d_3|u|^r$ with $rgeq 1$.