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This was later generalized to simplicial and reflexive pseudo-symmetric polytopes by (Ewald, 1988, 1996) in the smooth case, and by (Nill, 2006, Thm.
Classification of pseudo-symmetric simplicial reflexive polytopes.
They proved that the boundary value problem has at least three positive pseudo-symmetric solutions under some assumptions by using a pseudo-symmetric technique and the five-functionals fixed point theorem.
Su, Multiple positive pseudo-symmetric solutions of p-Laplacian dynamic equations on time scales, Math.