Ekeland Variational Principle for Generalized Vector Equilibrium Problems with Equivalences and Applications by De-ning Qu, Cao-zong Cheng

“…Finally, some equivalent results of the established Ekeland variational principle are presented.…”
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Vectorial Ekeland Variational Principles and Inclusion Problems in Cone Quasi-Uniform Spaces by Jiang Zhu, Lei Wei, Yeol Je Cho, Cheng Cheng Zhu

“…Some new vectorial Ekeland variational principles in cone quasi-uniform spaces are proved. …”
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Multiplicity of Homoclinic Solutions for a Class of Nonperiodic Fourth-Order Differential Equations with General Perturbation by Liu Yang

“…By using the mountain pass theorem and the Ekeland variational principle, we obtain that such equations possess two homoclinic solutions. …”
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Fixed point theorems in metric spaces and probabilistic metric spaces by Yeol Je Cho, Keun Saeng Park, Shih-Sen Chang

“…In this paper, we prove some common fixed point theorems for compatible mappings of type (A) in metric spaces and probabilistic metric spaces Also, we extend Caristi's fixed point theorem and Ekeland's variational principle in metric spaces to probabilistic metric spaces.…”
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Implicit Multifunction Theorems in Banach Spaces by Ming-ge Yang, Yi-fan Xu

“…The basic tools of our analysis involve the Ekeland variational principle, the Clarke subdifferential, and the Clarke coderivative.…”
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Variational Approaches to Characterize Weak Solutions for Some Problems of Mathematical Physics Equations by Irina Meghea

“…In this way generalized versions for some results which use Ekeland variational principle, critical points for nondifferentiable functionals, and Ghoussoub-Maurey linear principle have been proposed. …”
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The Existence of Cone Critical Point and Common Fixed Point with Applications by Wei-Shih Du

“…We first establish some new critical point theorems for nonlinear dynamical systems in cone metric spaces or usual metric spaces, and then we present some applications to generalizations of Dancš-Hegedüs-Medvegyev's principle and the existence theorem related with Ekeland's variational principle, Caristi's common fixed point theorem for multivalued maps, Takahashi's nonconvex minimization theorem, and common fuzzy fixed point theorem. …”
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A version of Zhong's coercivity result for a general class of nonsmooth functionals by D. Motreanu, V. V. Motreanu, D. Paşca

“…Our approach relies on a version of Ekeland's variational principle. In proving our coercivity result we make use of a new general Palais-Smale condition. …”
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Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity in R3 by Ling Ding, Lin Li, Jin-Ling Zhang

“…Under appropriate assumptions on k,f, and h, existence of two positive solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory.…”
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Multiple solutions for a problem with resonance involving the p-Laplacian by C. O. Alves, P. C. Carrião, O. H. Miyagaki

“…Using the Mountain Pass Theorem and the Ekeland Variational Principle, we will show the existence of at least three solutions for (P).…”
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Multiple positive solutions for a nonlocal problem with fast increasing weight and critical exponent by Xiaotao Qian, Zhigao Shi

“…By using the Ekeland variational principle and the concentration compactness principle, we establish the existence of two positive solutions for the problem and prove that at least one of them is a positive ground state solution.…”
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