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

2015 ◽  
Vol 2015 ◽  
pp. 1-4
Author(s):  
Mohammed El Mokhtar Ould El Mokhtar
Keyword(s):  
Variational Principle ◽  
Elliptic Equation ◽  
Critical Exponent ◽  
Elliptic Equations ◽  
Local Minimizer ◽  
Ekeland’S Variational Principle ◽  
Nontrivial Solutions ◽  
Ekeland's Variational Principle

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.

Existence and multiplicity of solutions for discontinuous elliptic problems in ℝ N

2020 ◽  
pp. 1-25
Author(s):  
Claudianor O. Alves ◽  
Ziqing Yuan ◽  
Lihong Huang
Keyword(s):  
Variational Principle ◽  
Variational Methods ◽  
Multiple Solutions ◽  
Elliptic Problems ◽  
Ekeland’S Variational Principle ◽  
Discontinuous Nonlinearity ◽  
Nontrivial Solutions ◽  
Ekeland's Variational Principle ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

Abstract This paper concerns with the existence of multiple solutions for a class of elliptic problems with discontinuous nonlinearity. By using dual variational methods, properties of the Nehari manifolds and Ekeland's variational principle, we show how the ‘shape’ of the graph of the function A affects the number of nontrivial solutions.

scholarly journals Multiple Nontrivial Solutions for a Class of Biharmonic Elliptic Equations with Sobolev Critical Exponent

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Xiaoyong Qian ◽  
Jun Wang ◽  
Maochun Zhu
Keyword(s):  
Elliptic Equation ◽  
Critical Exponent ◽  
Bounded Domain ◽  
Elliptic Equations ◽  
Nontrivial Solutions ◽  
Existence And Multiplicity ◽  
Sobolev Critical Exponent

In this paper, we study the existence and multiplicity of nontrivial solutions for a class of biharmonic elliptic equation with Sobolev critical exponent in a bounded domain. By using the idea of the previous paper, we generalize the results and prove the existence and multiplicity of nontrivial solutions of the biharmonic elliptic equations.

scholarly journals Remarks on Ume’s u−distance and Ekeland’s variational principle

2012 ◽  
Vol 28 (2) ◽  
pp. 257-264
Author(s):  
GEORGIANA GOGA ◽  
Keyword(s):  
Variational Principle ◽  
Ekeland’S Variational Principle ◽  
Ekeland's Variational Principle ◽  
Flower Petal ◽  
Flower Petal Theorem

The purpose of this paper is to present some remarks on Ume’s new concept of distance called u-distance, which generalizes w-distance and Suzuki’s t-distance. As an application of the u-distance version of Ekeland’s variational principle, we establish a generalized flower petal theorem.

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