Electronic Journal of Differential Equations,
Conference 05 (2000), pp. 325-333.

Title:  A condition on the potential for the existence of doubly 
        periodic solutions of a semi-linear fourth-order 
	partial differential equation

Author:   Chen Chang (Univ. of Texas at San Antonio, TX, USA)
 
Abstract: 
 We study the existence of solutions to the fourth order semi-linear 
 equation
$\Delta ^2u=g(u)+h(x)$.
We show that there is a positive constant $C_*$, such that if 
$g(\xi )\xi \geq 0$ for $|\xi |\geq \xi _0$ and 
$\limsup _{|\xi |\to \infty } 2G(\xi )/\xi^2<C_*$, then for all 
$h\in L^2(Q)$ with $\int _Q h dx=0$, the above equation has a 
weak solution in $H^2_{2\pi}$.

Published October 24, 2000.
Math Subject Classifications: 35J30, 35B10.
Key Words: periodic solutions; elliptic fourth-order PDE.