We show that the only locally integrable stationary solutions to the integrated Kuramoto-Sivashinsky equation in R and R2 are the trivial constant solutions. We extend our technique and prove similar results to other nonlinear elliptic problems in RN. © 2006 Elsevier Inc. All rights reserved.
Cao, Y., & Titi, E. S. (2006). Trivial stationary solutions to the Kuramoto-Sivashinsky and certain nonlinear elliptic equations. Journal of Differential Equations, 231(2), 755–767. https://doi.org/10.1016/j.jde.2006.08.002