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Variable order nonlocal Choquard problem with variable exponents

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TLDR
In this article, the existence/multiplicity results for the variable order nonlocal Choquard problem with variable exponents were studied and the existence and multiplicity results were derived.
Abstract
In this article, we study the existence/multiplicity results for the variable order nonlocal Choquard problem with variable exponents (−Δ)p(⋅)s(⋅)u(x)=λ|u(x)|α(x)−2u(x)+∫ΩF(y,u(y))|x−y|μ(x,y)dyf(x,...

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Existence and multiplicity results for p(⋅)&q(⋅) fractional Choquard problems with variable order

TL;DR: In this paper, the existence and multiplicity of solutions for the fractional variable order Choquard type problem was studied and the existence, multiplicity and existence of solutions were investigated.
Journal ArticleDOI

On a new fractional Sobolev space with variable exponent on complete manifolds

TL;DR: In this article , the theory of a new fractional Sobolev space in complete manifolds with variable exponent is presented, and the results of continuous and compact embedding results are valid.
Journal ArticleDOI

Strauss and Lions Type Theorems for the Fractional Sobolev Spaces with Variable Exponent and Applications to Nonlocal Kirchhoff–Choquard Problem

TL;DR: In this article, the Strauss and Lions-type theorems for fractional Sobolev spaces with variable exponent were dealt with and the existence of solutions for a class of Kirchhoff-Choquard problems was studied.
References
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Journal ArticleDOI

Hitchhiker's guide to the fractional Sobolev spaces

TL;DR: In this article, the authors deal with the fractional Sobolev spaces W s;p and analyze the relations among some of their possible denitions and their role in the trace theory.
Book

Lebesgue and Sobolev Spaces with Variable Exponents

TL;DR: In this paper, a framework for function spaces is presented, which includes variable exponent Lebesgue spaces, the maximal operator, the generalized Muckenhoupt condition, and transfer techniques.
Journal ArticleDOI

On the Spaces Lp(x)(Ω) and Wm, p(x)(Ω)

TL;DR: In this paper, the generalized Lebesgue spaces L-p(x)(Omega) and generalized lebesgue-Sobolev spaces W-m,W-p (x) were studied.
Journal ArticleDOI

Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation

TL;DR: In this article, the Hartree-Fock theory of a plasma was used to prove existence and uniqueness of a minimization of the functional function of an electron trapped in its own hole.
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