Results 1 to 10 of about 465 (165)

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.
S. Cobzaş, Cobzaş, S.
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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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Vectorial Form of Ekeland-Type Variational Principle in Locally Convex Spaces and Its Applications

Fixed Point Theory and Applications, 2010
By using a Dane ' drop theorem in locally convex spaces we obtain a vectorial form of Ekeland-type variational principle in locally convex spaces. From this theorem, we derive some versions of vectorial Caristi-Kirk's fixed-point theorem, Takahashi's ...
Eshghinezhad S, Fakhar M
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Multiple solutions for nonlinear discontinuous strongly resonant elliptic problems

Abstract and Applied Analysis, 2000
We consider quasilinear strongly resonant problems with discontinuous right-hand side. To develop an existence theory we pass to a multivalued problem by, roughly speaking, filling in the gaps at the discontinuity points.
Nikolaos C. Kourogenis, Nikolaos S. Papageorgiou   +1 more
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Existence of nontrivial solutions for a fractional p & q $p\&q$ -Laplacian equation with sandwich-type and sign-changing nonlinearities

Journal of Inequalities and Applications
In this paper, we deal with the following fractional p & q $p\&q$ -Laplacian problem: { ( − Δ ) p s u + ( − Δ ) q s u = λ a ( x ) | u | θ − 2 u + μ b ( x ) | u | r − 2 u in Ω , u ( x ) = 0 in R N ∖ Ω , $$ \left \{ \textstyle\begin{array}{l@{\quad }l ...
Qin Li, Zonghu Xiu, Lin Chen
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Multiple positive solutions for Kirchhoff type problems involving concave and convex nonlinearities in R^3

Electronic Journal of Differential Equations, 2016
In this article, we consider the multiplicity of positive solutions for a class of Kirchhoff type problems with concave and convex nonlinearities. Under appropriate assumptions, we prove that the problem has at least two positive solutions, moreover ...
Xiaofei Cao, Junxiang Xu, Jun Wang
doaj  

A generalization of Ekeland's variational principle with applications

Electronic Journal of Differential Equations, 2006
Summary: In this paper, we establish a variant of Ekeland's variational principle. This result suggest to introduce a generalization of the famous Palais-Smale condition. An example is provided showing how it is used to give the existence of a minimizer for functions for which the Palais-Smale condition and the one introduced by Cerami are not ...
Abdel R. El Amrouss, Najib Tsouli
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Towards a simple mathematical theory of citation distributions. [PDF]

Springerplus, 2015
Katchanov YL.
europepmc   +1 more source

Solutions for the quasi-linear elliptic problems involving the critical Sobolev exponent. [PDF]

J Inequal Appl, 2017
Sang Y, Guo S.
europepmc   +1 more source

A generalization of Ekeland's variational principle by using the τ-distance with its applications. [PDF]

J Inequal Appl, 2017
Farajzadeh AP, Plubtieng S, Hoseinpour A.   +2 more
europepmc   +1 more source