SINGULAR LIMIT SOLUTIONS FOR 4-DIMENSIONAL STATIONARY KURAMOTO-SIVASHINSKY EQUATIONS WITH EXPONENTIAL NONLINEARITY

Let Omega be a bounded domain in R-4 with smooth boundary, and let x(1), x(2), ... , x(m) be points in Omega. We are concerned with the singular stationary non-homogenous Kuramoto-Sivashinsky equation Delta(2)u - gamma Delta u - lambda vertical bar del u vertical bar(2) = rho(4)f(u), where f is a function that depends only the spatial variable. We use a nonlinear domain decomposition method to give su ffi cient conditions for the existence of a positive weak solution satisfying the Dirichlet-like boundary conditions u = Delta u = 0, and being singular at each x(i) as the parameters lambda, gamma and rho tend to 0. An analogous problem in two-dimensions was considered in [2] under condition (A1) below. However we do not assume this condition.