Harnack‐type inequality for fractional elliptic equations with critical exponent

2020 ◽  
Vol 43 (8) ◽  
pp. 5380-5397 ◽  
Author(s):  
Shuibo Huang ◽  
Qiaoyu Tian
Keyword(s):  
Critical Exponent ◽  
Elliptic Equations ◽  
Type Inequality ◽  
Harnack Type Inequality

scholarly journals Multiple of Solutions for Nonlocal Elliptic Equations with Critical Exponent Driven by the Fractional p-Laplacian of Order s

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
M. Khiddi
Keyword(s):  
Variational Methods ◽  
Critical Exponent ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Nehari Manifold ◽  
Lusternik Schnirelmann ◽  
The Nehari Manifold

In this paper, we study the existence of infinitely many weak solutions for nonlocal elliptic equations with critical exponent driven by the fractional p-Laplacian of order s. We show the above result when λ>0 is small enough. We achieve our goal by making use of variational methods, more specifically, the Nehari Manifold and Lusternik-Schnirelmann theory.

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.

Generalized Olsen inequality and Schrödinger type elliptic equations

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Yuxing Guo
Keyword(s):  
Elliptic Equations ◽  
Morrey Space ◽  
Riesz Potential ◽  
Type Inequality ◽  
Hölder Condition ◽  
Generalized Morrey Space ◽  
Interior Estimates ◽  
Reverse Hölder

Abstract In this paper, by means of the generalized Olsen type inequality, related to the Riesz potential and its commutators, the author establishes the interior estimates on the generalized Morrey space for Schrödinger type elliptic equations with potentials satisfying the reverse Hölder condition.

Sign in / Sign up

Export Citation Format

Share Document