scholarly journals The concentration-compactness principles for Ws,p(·,·)(ℝN) and application

2020 ◽  
Vol 10 (1) ◽  
pp. 816-848
Author(s):  
Ky Ho ◽  
Yun-Ho Kim
Keyword(s):  
Sobolev Spaces ◽  
Concentration Compactness ◽  
Variable Exponents ◽  
Fractional Sobolev Spaces ◽  
Nonlocal Problems

Abstract We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems with variable exponents, which is even new for constant exponent case.

A Critical Point Theorem for Perturbed Functionals and Low Perturbations of Differential and Nonlocal Systems

2020 ◽  
Vol 20 (3) ◽  
pp. 663-674 ◽  
Author(s):  
Anouar Bahrouni ◽  
Vicenţiu D. Rădulescu ◽  
Patrick Winkert
Keyword(s):  
Critical Point ◽  
Point Theorem ◽  
Sobolev Spaces ◽  
Fractional Sobolev Spaces ◽  
Nonlocal Problems ◽  
Abstract Result ◽  
Critical Point Theorem ◽  
Palais Smale Condition

AbstractIn this paper we establish a new critical point theorem for a class of perturbed differentiable functionals without satisfying the Palais–Smale condition. We prove the existence of at least one critical point to such functionals, provided that the perturbation is sufficiently small. The main abstract result of this paper is applied both to perturbed nonhomogeneous equations in Orlicz–Sobolev spaces and to nonlocal problems in fractional Sobolev spaces.

Compact embedding theorems for fractional Sobolev spaces with variable exponents

2019 ◽  
Vol 5 (1) ◽  
pp. 83-93
Author(s):  
Mohamed Berghout ◽  
Azeddine Baalal
Keyword(s):  
Sobolev Spaces ◽  
Compact Embedding ◽  
Variable Exponents ◽  
Embedding Theorems ◽  
Fractional Sobolev Spaces

Density properties for fractional Sobolev spaces with variable exponents

2019 ◽  
Vol 10 (3) ◽  
pp. 308-324 ◽  
Author(s):  
Azeddine Baalal ◽  
Mohamed Berghout
Keyword(s):  
Sobolev Spaces ◽  
Variable Exponents ◽  
Fractional Sobolev Spaces

scholarly journals Composition in fractional Sobolev spaces

2001 ◽  
Vol 7 (2) ◽  
pp. 241-246 ◽  
Author(s):  
Haim Brezis ◽  
◽  
Petru Mironescu ◽  
Keyword(s):  
Sobolev Spaces ◽  
Fractional Sobolev Spaces

Generalized Gagliardo–Nirenberg inequalities using Lorentz spaces, BMO, Hölder spaces and fractional Sobolev spaces

2018 ◽  
Vol 173 ◽  
pp. 146-153 ◽  
Author(s):  
Nguyen Anh Dao ◽  
Jesus Ildefonso Díaz ◽  
Quoc-Hung Nguyen
Keyword(s):  
Sobolev Spaces ◽  
Lorentz Spaces ◽  
Fractional Sobolev Spaces ◽  
Hölder Spaces ◽  
Holder Spaces

Existence Results for Nonlinear Elliptic Equations with Leray–Lions Operators in Sobolev Spaces with Variable Exponents

2021 ◽  
Vol 110 (5-6) ◽  
pp. 830-841
Author(s):  
M. Mosa Al-Shomrani ◽  
M. Ben Mohamed Salah ◽  
A. Ghanmi ◽  
K. Kefi
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Existence Results ◽  
Variable Exponents ◽  
Nonlinear Elliptic
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