W1,p versus C1 local minimizers and multiplicity results for quasilinear elliptic equations

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Multiple Solutions for Nonlinear Coercive Problems with a Nonhomogeneous Differential Operator and a Nonsmooth Potential (2012, background): “It was extended to the case G(y) = 1 p ‖y‖p, with 1 < p < +∞ and smooth functionals by García Azorero-Manfredi-Peral Alonso [15] (see also Guo-Zhang [21], where p 2).”
Multiple positive solutions of singular-Laplacian problems by variational methods (2005, unknown): “6) Φλ,2u = Φλ in a C 0(Ω)-neighborhood of u0, so u0 is a local minimizer of Φλ|C1 0(Ω), and hence also of Φλ by Brezis and Nirenberg [3] for p = 2 and by Guo and Zhang [9] for p > 2.”