Results 31 to 40 of about 1,030,362 (113)

Ekeland's variational principle, minimax theorems and existence of nonconvex equilibria in complete metric spaces [PDF]

, 2006
In this paper, we introduce the concept of τ-function which generalizes the concept of w-distance studied in the literature. We establish a generalized Ekeland's variational principle in the setting of lower semicontinuous from above and τ-functions.
Lin, Lai-Jiu, Du, Wei-Shih
core   +1 more source

Maximum principle for near-optimality of stochastic delay control problem

Advances in Difference Equations, 2017
This paper is concerned with near-optimality for stochastic control problems of linear delay systems with convex control domain and controlled diffusion. Necessary and sufficient conditions for a control to be near-optimal are established by Pontryagin’s
Feng Zhang
doaj   +1 more source

Caffarelli–Kohn–Nirenberg inequality for biharmonic equations with inhomogeneous term and Rellich potential

Electronic Journal of Qualitative Theory of Differential Equations, 2023
In this article, multiplicity of nontrivial solutions for an inhomogeneous singular biharmonic equation with Rellich potential are studied. Firstly, a negative energy solution of the studied equations is achieved via the Ekeland's variational principle ...
Yang Yu, Yulin Zhao
doaj   +1 more source

Ekeland's variational principle and its equivalent theorems in vector optimization [PDF]

, 2008
We present a simple proof of vectorial Ekeland's variational principle, vectorial Caristi's fixed point theorem and vectorial Takahashi's nonconvex minimization theorem.
Araya, Yousuke, Yousuke Araya
core   +1 more source

Some new results on stability of Ekeland's ϵ-variational principle [PDF]

, 2008
In this paper, we give an example and point out that ϵ-solutions of Ekeland's variational principle are not always lower semicontinuous in infinite-dimensional Banach spaces, even with respect to the uniform metric.
Wang, Changchun, Yin, Wen-Shuang, Xiang, Shu-Wen   +2 more
core   +1 more source

A minimization theorem in quasi-metric spaces and its applications

International Journal of Mathematics and Mathematical Sciences, 2002
We prove a new minimization theorem in quasi-metric spaces, which improves the results of Takahashi (1993). Further, this theorem is used to generalize Caristi's fixed point theorem and Ekeland's ϵ-variational principle.
Jeong Sheok Ume
doaj   +1 more source

Multiple positive solutions for quasilinear elliptic problems with combined critical Sobolev–Hardy terms

Boundary Value Problems, 2019
In this paper, we investigate the quasilinear elliptic equations involving multiple critical Sobolev–Hardy terms with Dirichlet boundary conditions on bounded smooth domains  Ω⊂RN $\varOmega \subset R^{N}$ ( N≥3 ${N \ge 3} $), and prove the multiplicity ...
Yuanyuan Li
doaj   +1 more source

Existence for Elliptic Equation Involving Decaying Cylindrical Potentials with Subcritical and Critical Exponent

International Journal of Differential Equations, 2015
We consider the existence of nontrivial solutions to elliptic equations with decaying cylindrical potentials and subcritical exponent. We will obtain a local minimizer by using Ekeland’s variational principle.
Mohammed El Mokhtar Ould El Mokhtar
doaj   +1 more source

Critical point result of Schechter type in a Banach space

Electronic Journal of Qualitative Theory of Differential Equations, 2016
Using Ekeland's variational principle we give a critical point theorem of Schechter type for extrema on a sublevel set in a Banach space. This result can be applied to localize the solutions of PDEs which contain nonlinear homogeneous operators.
Hannelore Lisei, Orsolya Vas
doaj   +1 more source

One remark to Ekeland's variational principle [PDF]

, 1997
This article deals with the generalization of Ekeland's first-order necessary conditions of minimum. They are extended to include second-order conditions.
Bobylev, N., Arutyunov, A., A. Arutyunov, Korovin, S., S. Korovin, N. Bobylev   +5 more
core   +1 more source