Fixed-Point Results and the Ekeland Variational Principle in Vector B-Metric Spaces
AxiomsIn 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.
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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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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 $$\displaylines{ -\Big(a+b\int_{\Omega}|\nabla u|^2dx \Big) \Delta u =b \mu u^3+f(x,u)+h(x), \quad\text{in
Shu-Zhi Song +2 more
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Infinitely many homoclinic solutions for second order nonlinear difference equations with p-Laplacian. [PDF]
ScientificWorldJournal, 2014 Sun G, Mai A.
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Existence and multiplicity of solutions for nonhomogeneous Klein-Gordon-Maxwell equations
Electronic Journal of Differential Equations, 2015 This article concerns the nonhomogeneous Klein-Gordon-Maxwell equation $$\displaylines{ -\Delta u+u-(2\omega +\phi)\phi u=|u|^{p-1}u +h(x), \quad\text{in }\mathbb{R}^3,\cr \Delta \phi=(\omega +\phi)u^2,\quad\text{in }\mathbb{R}^3, }$$ where ...
Liping Xu, Haibo Chen
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A Constructive Version of Ekeland's Variational Principle
Building on preliminary results about lower sections of real-valued functions on a metric space, we provide a constructive counterpart of Ekeland's theorem on the approximate optimisation of real-valued functions.
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Existence and multiplicity of solutions to triharmonic problems
Electronic Journal of Differential EquationsThe authors consider the triharmonic equation $$ (-\Delta)^3u+c_1\Delta^2 u+c_2\Delta u=h(x)|u|^{p-2} u+g(x,u) $$ in $\Omega$, where $p\in(1,2)$, subject to Navier boundary conditions.
Qifan Wei, Xuemei Zhang
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On some fixed point results using CG simulation functions via w-distance with applications. [PDF]
HeliyonAtallaoui S +4 more
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Time optimal controls of the linear Fitzhugh-Nagumo equation with pointwise control constraints.
J Math Anal Appl, 2012 Kunisch K, Wang L.
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