Results 111 to 120 of about 585 (200)

A Survey of Ekeland's Variational Principle and Related Theorems and Applications

, 2020
Jessica Robinson
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A generalization of the Ekeland variational principle

, 2020
In this short communication, we present a generalization of the Ekeland variational principle. The main result is established through standard tools of functional analysis and calculus of variations. The novelty here is a result involving the second G teaux variation of the functional in question.
openaire   +2 more sources

Graphical Ekeland's variational principle with a generalized $w$-distance and a new approach to quasi-equilibrium problems

, 2022
", Parin Chaipunya, Nantaporn Chuensupantharat, PRINTAPORN SANGUANSUTTIGUL   +3 more
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Positive Ground State Solutions for Fractional (p, q)-Laplacian Choquard Equation with Singularity and Upper Critical Exponent

Fractal and Fractional
We prove the existence of a positive ground state solution for a fractional (p,q)-Laplacian Choquard equation that features both a singularity and an upper critical exponent.
Zhenyu Bai, Chuanzhi Bai
doaj   +1 more source

Some Notes on τ-Distance Versions of Ekeland's Variational Principle [PDF]

, 2009
Tomonari Suzuki
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Completeness in quasi-metric spaces and Ekeland Variational Principle

Topology and its Applications, 2011
The author establishes a quasi-metric version of the Ekeland variational principle and studies its connections with the completeness properties of the underlying quasi-metric space. The equivalence with Caristi-Kirk's fixed point theorem and a proof of Clarke's fixed point theorem for directional contractions within this framework are also investigated.
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Fixed-Point Results and the Ekeland Variational Principle in Vector B-Metric Spaces

Axioms
In this paper, we extend the concept of b-metric spaces to the vectorial case, where the distance is vector-valued, and the constant in the triangle inequality axiom is replaced by a matrix. For such spaces, we establish results analogous to those in the
Radu Precup, Andrei Stan
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Multiplicity and asymptotic behavior of solutions for Kirchhoff type equations involving the Hardy-Sobolev exponent and singular nonlinearity. [PDF]

J Inequal Appl, 2018
Shen L.
europepmc   +1 more source

Multiple solutions for Kirchhoff type problem near resonance

Electronic Journal of Differential Equations, 2015
Based on Ekeland's variational principle and the mountain pass theorem, we show the existence of three solutions to the Kirchhoff type problem $$\displaylines{ -\Big(a+b\int_{\Omega}|\nabla u|^2dx \Big) \Delta u =b \mu u^3+f(x,u)+h(x), \quad\text{in
Shu-Zhi Song, Chun-Lei Tang, Shang-Jie Chen   +2 more
doaj  

Infinitely many homoclinic solutions for second order nonlinear difference equations with p-Laplacian. [PDF]

ScientificWorldJournal, 2014
Sun G, Mai A.
europepmc   +1 more source