Results 41 to 50 of about 343 (158)

On p‐Laplace Equations with Singular Nonlinearities and Critical Sobolev Exponent

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
In this paper, we deal with p‐Laplace equations with singular nonlinearities and critical Sobolev exponent. By using the Nehari manifold, Mountain Pass theorem, and Maximum principle theorem, we prove the existence of at least four distinct nontrivial solutions.
Mohammed El Mokhtar ould El Mokhtar, Andrea Scapellato   +1 more
wiley   +1 more source

Existence of solution for a Kirchhoff type problem involving the fractional p-Laplace operator

Electronic Journal of Qualitative Theory of Differential Equations, 2015
This paper is concerned with the existence of solutions to a Kirchhoff type problem involving the fractional $p$-Laplacian operator. We obtain the existence of solutions by Ekeland's variational principle.
Wenjing Chen, Shengbing Deng
doaj   +1 more source

On Ekeland's Variational Principle in Partial Metric Spaces

, 2015
In this paper, lower semi-continuous functions are used to extend Ekeland's variational principle to the class of partial metric spaces. As consequences of our results, we obtain some fixed point theorems of Caristi and Clarke types.
Vetro,C., Aydi,H., Karapinar,E., Karapınar, Erdal   +3 more
core   +2 more sources

The Multiplicity of Nontrivial Solutions for a New px-Kirchhoff-Type Elliptic Problem

Journal of Function Spaces, 2021
In the paper, we study the existence of weak solutions for a class of new nonlocal problems involving a px-Laplacian operator. By using Ekeland’s variational principle and mountain pass theorem, we prove that the new px-Kirchhoff problem has at least two
Chang-Mu Chu, Yu-Xia Xiao
doaj   +1 more source

On Ekeland's variational principle for interval-valued functions with applications [PDF]

Fuzzy Sets and Systems, 2022
In this paper, we obtain a version of Ekeland's variational principle for interval-value functions by means of the Dancs-Hegedus-Medvegyev theorem [14]. We also derive two versions of Ekeland's variational principle involving the generalized Hukuhara Gateaux differentiability of interval-valued functions as well as a version of Ekeland's variational ...
Chuangliang Zhang, Nan-jing Huang
openaire   +3 more sources

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

On Ekeland’s Variational Principle in Rectangular bmertic Spaces

Journal of Harbin University of Science and Technology, 2020
Ekeland′s variational principle plays an important role in fixed point theory. It has applications in many fields such as optimization theory, control theory, critical point theory and others.
HUANG Shuai, CHEN Lili, LIU Xin
doaj   +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

Ekeland’s variational principle in weak and strong systems of arithmetic [PDF]

Selecta Mathematica, 2020
AbstractWe analyze Ekeland’s variational principle in the context of reverse mathematics. We find that that the full variational principle is equivalent to $$\Pi ^1_1\text{- }\mathsf {CA}_0$$ Π 1 1 - CA 0 , a strong theory of second-order arithmetic, while natural restrictions (e.g.
David Fernández-Duque, Paul Shafer, Keita Yokoyama   +2 more
openaire   +4 more sources

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