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