Existence and multiplicity of solutions for Neumann problems

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Existence of three nontrivial solutions for nonlinear Neumann hemivariational inequalities (2009, methodology): “Also in Filippakis–Gasiński–Papageorgiou [13] and in Motreanu–Papageorgiou [22] problems with nonsmooth potentials are examined and, following an approach based on the nonsmooth critical point theory, two or infinitely many solutions are obtained.”
Existence of multiple solutions with precise sign information for superlinear Neumann problems (2009, background): “Kyritsi, S., Papageorgiou, N.S.: Multiple solutions of constant sign for nonlinear nonsmooth eigenvalue problems near resonance.”
Multiple solutions for nonlinear Neumann problems driven by a nonhomogeneous differential operator (2011, background): “Some recent multiplicity results for the Neumann problem deal with equations involving the p-Laplacian, but they impose the restrictive condition p > N or are related to parameters (see [2, 7, 19, 21]).”