Trivial Stationary Solutions to the Kuramoto-Sivashinsky and Certain   Nonlinear Elliptic Equations
  We show that the only locally integrable stationary solutions to the integrated Kuramoto-Sivashinsky equation in $R$ and $R^2$ are the trivial constant solutions. We extend our technique and prove similar results to other nonlinear elliptic problems in $\R^N$. 
Yanping Cao and Edriss S. Titi