The Functionalized Cahn-Hilliard (FCH) energy is a model describing the interfacial energy in a phase separated mixture of amphiphilic molecules and a solvent. On a bounded domain in R, the Euler-Lagrange equation for the mass constrained Functionalized Cahn-Hilliard(FCH) free energy with zero functionalization terms is derived and a large family of multi-pulse critical points is constructed. We show that the FCH energy with no functiona-lization terms subject to a mass constraint has global minimizers over a variety of admissible sets. We introduce a multi-pulse ansatz as the extensions of the periodic multi-pulse critical points to R and establish the H^2-coercivity of the second variation of the energy about multi-pulse ansatz. Modulational stability and the dynamic evolution of the multi-pulse ansatz with respect to the Pi_0-gradient flow are also addressed.
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