Nonlinear Differential Equations,

Electron. J. Diff. Eqns., Conf. 05, 2000, pp. 325-333.

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

Chen Chang

**Abstract:**

We study the existence of solutions to the fourth order semi-linear equation

.

We show that there is a positive constant
,
such that if
for
and
,
then for all
with
,
the above equation has a weak solution in
.
Published October 31, 2000.

Math Subject Classifications: 35J30, 35B10.

Key Words: periodic solutions, elliptic fourth-order PDE.

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Chen Chang

Division of Mathematics and Statistics

the University of Texas at San Antonio

San Antonio, TX 78249 USA

e-mail: chang@math.utsa.edu

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