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.…”
Get full text

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. …”
Get full text

From Caristi’s Theorem to Ekeland’s Variational Principle in 0σ-Complete Metric-Like Spaces by Mohamed Jleli, Bessem Samet, Calogero Vetro, Francesca Vetro

Get full text

The Interconnection Between Calculus of Variations, Partial Differential Equations and Differential Geometry by Delphin Mwinken

Subjects: Get full text

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. …”
Get full text

Stochastic Maximum Principle of Near-Optimal Control of Fully Coupled Forward-Backward Stochastic Differential Equation by Maoning Tang

“…This paper first makes an attempt to investigate the near-optimal control of systems governed by fully nonlinear coupled forward-backward stochastic differential equations (FBSDEs) under the assumption of a convex control domain. By Ekeland’s variational principle and some basic estimates for state processes and adjoint processes, we establish the necessary conditions for any ε-near optimal control in a local form with an error order of exact ε1/2. …”
Get full text

Multiple positive solutions for a nonlocal problem with fast increasing weight and critical exponent by Xiaotao Qian, Zhigao Shi

“…Abstract In this paper, we are concerned with the following nonlocal problem: − ( a − ϵ ∫ R 3 K ( x ) | ∇ u | 2 d x ) div ( K ( x ) ∇ u ) = λ K ( x ) f ( x ) | u | q − 2 u + K ( x ) | u | 4 u , x ∈ R 3 , $$ -\left (a-\epsilon \displaystyle \int _{\mathbb{R}^{3}} K(x)| \nabla u|^{2}dx\right )\text{div}(K(x)\nabla u)=\lambda K(x)f(x)|u|^{q-2}u+K(x)|u|^{4}u, \quad x\in \mathbb{R}^{3}, $$ where a , λ > 0 $a, \lambda >0$ , 1 < q < 2 $1< q<2$ , K ( x ) = exp ( | x | α / 4 ) $K(x)=\exp ({|x|^{\alpha}/4})$ with α ≥ 2 $\alpha \geq 2$ , ϵ > 0 $\epsilon >0$ is small enough, and f ( x ) ≥ 0 $f(x)\ge 0$ satisfies some integrability condition. 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.…”
Get full text

Existence for Elliptic Equation Involving Decaying Cylindrical Potentials with Subcritical and Critical Exponent by Mohammed El Mokhtar Ould El Mokhtar

“…We will obtain a local minimizer by using Ekeland’s variational principle.…”
Get full text

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. …”
Get full text

Concerning Kirk’s problem by Hamid Mottaghi Golshan

“…Additionally, a new proof provides an affirmative answer to Kirk’s problem, supported by examples. Finally, Ekeland’s variational principle (abbreviated EVP) is developed.…”
Get full text

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. …”
Get full text

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.…”
Get full text

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.…”
Get full text

Multiplicity Results for Variable-Order Nonlinear Fractional Magnetic Schrödinger Equation with Variable Growth by Jianwen Zhou, Bianxiang Zhou, Yanning Wang

“…Under appropriate assumptions, firstly, we prove that the system has at least two different solutions by applying the mountain pass theorem and Ekeland’s variational principle. Secondly, we prove that these two solutions converge to the two solutions of the limit problem. …”
Get full text

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. …”
Get full text

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.…”
Get full text

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).…”
Get full text

Negative Energy Solutions for a New Fractional px-Kirchhoff Problem without the (AR) Condition by Weichun Bu, Tianqing An, Guoju Ye, Said Taarabti

“…In this paper, we investigate the following Kirchhoff type problem involving the fractional px-Laplacian operator. a−b∫Ω×Ωux−uypx,y/px,yx−yN+spx,ydxdyLu=λuqx−2u+fx,ux∈Ωu=0 x∈∂Ω,, where Ω is a bounded domain in ℝN with Lipschitz boundary, a≥b>0 are constants, px,y is a function defined on Ω¯×Ω¯, s∈0,1, and qx>1, Lu is the fractional px-Laplacian operator, N>spx,y, for any x,y∈Ω¯×Ω¯, px∗=px,xN/N−spx,x, λ is a given positive parameter, and f is a continuous function. By using Ekeland’s variational principle and dual fountain theorem, we obtain some new existence and multiplicity of negative energy solutions for the above problem without the Ambrosetti-Rabinowitz ((AR) for short) condition.…”
Get full text