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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 to a class of Kirchhoff-type equations involving the fractional p-Laplacian. [PDF]

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

Towards a simple mathematical theory of citation distributions. [PDF]

Springerplus, 2015
Katchanov YL.
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  

Maximizing tree harvesting benefit from forests under insect infestation disturbances. [PDF]

PLoS One, 2018
Leite MCA, Chen-Charpentier B, Agusto FB.   +2 more
europepmc   +1 more source

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
doaj  

Existence and multiplicity of solutions to triharmonic problems

Electronic Journal of Differential Equations
The 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
doaj  

Time optimal controls of the linear Fitzhugh-Nagumo equation with pointwise control constraints.

J Math Anal Appl, 2012
Kunisch K, Wang L.
europepmc   +1 more source

Existence of normalized solutions to Kirchhoff-Boussinesq equations in the subcritical and supercritical regime

Electronic Journal of Differential Equations
In this article we study the existence of normalized solutions to the Kirchhoff-Boussinesq equation under the mass constraint $\|u\|_{2}=c$. In the $L^{2}$-subcritical regime, we apply Ekeland's variational principle and concentration compactness method ...
Chunling Tao, Lintao Liu, Kaimin Teng
doaj  

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Are several recent generalizations of Ekeland's variational principle more general than the original principle?

2003
This paper is related to the works [\textit{C.-K. Zhong}, ``A generalization of Ekeland's variational principle and application to the study of the relation between the weak P. S. condition and coercivity'', Nonlinear Anal., Theory Methods Appl. 29, No. 12, 1421--1431 (1997; Zbl 0912.49021)] and [\textit{J. Zhu, C.-K. Zhong} and \textit{Y. J.
Bao, Truong Q, Khanh, Phan Q
openaire   +1 more source