Ekeland’s Variational Principle and Its Extensions with Applications

2013 ◽  
pp. 65-100 ◽  
Author(s):  
Qamrul Hasan Ansari
Keyword(s):  
Variational Principle ◽  
Ekeland’S Variational Principle ◽  
Ekeland's Variational Principle

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.

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.

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