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Later, the famous Brézis-Browder's maximal element principle [5] was established and applied to deal with nonlinear problems.
In [7] (see also [3]), Lin and Du established the following abstract maximal element principle in a -bounded quasiordered set with a sizing-up function.
Many generalizations in various different directions of maximal element principle have been studied in the past; for example, see [2, 3, 6 10] and references therein.
By applying Theorem LD, Du [7] gave a generalized Brézis-Browder principle, system (vectorial) versions of Ekeland's variational principle and maximal element principle and a vectorial version of Takahashi's nonconvex minimization theorem.
We present some new critical point theorems for nonlinear dynamical systems which are generalizations of Dancš-Hegedüs-Medvegyev Dancš-Hegedüs-Medvegyev Dancš-Hegedüs-Medvegyev by applying an abstract maximal element principle established by Lin and Du.
In 1963, Bishop and Phelps [4] proved a fundamental theorem concerning the density of the set of support points of a closed convex subset of a Banach space by using a maximal element principle in certain partially ordered complete subsets of a normed linear space.
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