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Solutions of the stationary semilinear Cahn-Hilliard-type equation−Delta2u−u−Delta(|u|p−1u)=0in RN,with p>1,−Delta2u−u−Delta(|u|p−1u)=0in RN,with p>1,which are exponentially decaying at infinity, are studied. Using the mounting pass lemma allows us to determinate the existence of a radially symmetric solution. On the other hand, the application of Lusternik-Schnirel'man (L-S) category theory shows the existence of, at least, a countable family of solutions.However, through numerical methods it is shown that the whole set of solutions, even in 1D, is much wider. This suggests that, actually, there exists, at least, a countable set of countable families of solutions, in which only the first one can be obtained by the L-S min-max approach.
stationary cahn-hilliard equation; variational setting; non-unique oscillatory solutions; countable family of critical points