Existence of two weak solutions for biharmonic equations with the Hardy-Sobolev critical exponent and non-homogeneous perturbation term

2019 ◽  
Vol 49 (12) ◽  
pp. 1813
Author(s):  
Yang Tao ◽  
Huang Anlang ◽  
Li Gongbao
Keyword(s):  
Critical Exponent ◽  
Weak Solutions ◽  
Biharmonic Equations ◽  
Perturbation Term ◽  
Sobolev Critical Exponent

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 On Local Weak Solutions for Fractional in Time SOBOLEV-Type Inequalities

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Mohaemd Jleli ◽  
Bessem Samet
Keyword(s):  
Critical Exponent ◽  
Weak Solutions ◽  
Fractional Derivatives ◽  
Sobolev Type ◽  
Existence And Nonexistence

We consider two fractional in time nonlinear Sobolev-type inequalities involving potential terms, where the fractional derivatives are defined in the sense of Caputo. For both problems, we study the existence and nonexistence of nontrivial local weak solutions. Namely, we show that there exists a critical exponent according to which we have existence or nonexistence.

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