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We give a multiplicity result for solutions of the Van derWaals-Cahn-Hilliard two-phase transition equation with volume constraints on aclosed Riemannian manifold. Our proof employs some results from the classicalLusternik--Schnirelman and Morse theory, together with a technique, theso-called \emph{photography method}, which allows us to obtain lower bounds onthe number of solutions in terms of topological invariants of the underlyingmanifold. The setup for the photography method employs recent results fromRiemannian isoperimetry for small volumes.

Lusternik-Schnirelman and Morse theory for the Van der Waals-Cahn-Hilliard equation with volume constraint