About the Stochastic ~u~tip~cative Swift-~ohenberg Equation: The Eigenvalue Problem

The eigenvalues of the Swift-Hohenberg operator in d-dim and for piece wise constant potentials has been solved by a mapping procedure. Some analytic eigenvalues have been compared with their numerical results and shown to be in very good agreement. Furthermore, striking behaviours for the number of nodes of the Swift-Hohenberg ground state has been point