On the structure of the critical set of non-differentiable functions with a weak compactness condition

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Existence and multiplicity of weak solutions for elliptic Dirichlet problems with variable exponent (2014, background): “Marano in [6], that we recall in a convenient form.”
Existence of three solutions for a non-homogeneous Neumann problem through Orlicz–Sobolev spaces (2011, background): “This result has been obtained in [37] and it is a more precise version of Theorem 3.”
Variational Methods on Finite Dimensional Banach Spaces and Discrete Problems (2014, background): “The proofs of these theorems are simpler than the corresponding infinite dimensional cases given in [4], [5] and [11], just because the finite dimensional setting is fully exploited.”