Ljusternik-Schnirelman theory in partially ordered Hilbert spaces

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Multiplicity results for a class of superlinear elliptic problems (2004, methodology): “We employ the method in [4].”
Sign Changing Solutions of Superlinear Schrödinger Equations (2003, methodology): “The methods and the abstract critical point theory from Bartsch (2001) and Bartsch and Wang (1999) or Li and Wang (2000, 2002) require to work on a Banach space X ⊂ H1 whose cone of positive functions has nonempty interior.”
Multiple Sign-Changing Solutions for Quasilinear Elliptic Equations via Perturbation Method (2014, methodology): “We refer signchanging solutions to [5, 17, 18] for more references therein.”
Schrödinger equations with concave and convex nonlinearities (2005, background): “The main idea in [3, 17, 27, 28 , 29] is to make use of the cones of positive functions and negative functions in C 1 0 (Ω).”
Existence of five nonzero solutions with exact sign for A p-laplacian equation (2009, methodology): “Roughly speaking, from these works emerged two approaches to the problem: (a) combining the method of upper-lower solutions with variational techniques (see Dancer-Du [18, 19, 20]); (b) using invariance properties of the negative gradient flow associated to a well-chosen pseudo-gradient vector field”