Results 41 to 50 of about 131 (87)
Orlicz norm inequalities for the composite operator and applications
Journal of Inequalities and Applications, 2011 In this article, we first prove Orlicz norm inequalities for the composition of the homotopy operator and the projection operator acting on solutions of the nonhomogeneous A-harmonic equation.
Ding Shusen, Bi Hui
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Some remarks about the summability of nonlocal nonlinear problems
Advances in Nonlinear Analysis, 2015 In this note, we will study the problem (-Δ)psu = f(x) on Ω, u = 0 in ℝN∖Ω, where 0 < s < 1, (-Δ)ps is the nonlocal p-Laplacian defined below, Ω is a smooth bounded domain. The main point studied in this work is to prove, adapting the techniques used in [
Barrios Begoña +2 more
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Advances in Nonlinear Analysis, 2022 In this article, we study the existence of multiple solutions to a generalized p(⋅)p\left(\cdot )-Laplace equation with two parameters involving critical growth.
Ho Ky, Sim Inbo
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Inequalities for Green's operator applied to the minimizers
Journal of Inequalities and Applications, 2011 In this paper, we prove both the local and global Lφ -norm inequalities for Green's operator applied to minimizers for functionals defined on differential forms in Lφ -averaging domains.
Ding Shusen, Agarwal Ravi
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Remarks on a nonlinear nonlocal operator in Orlicz spaces
Advances in Nonlinear Analysis, 2019 We study integral operators Lu(χ)=∫ℝℕψ(u(x)−u(y))J(x−y)dy$\mathcal{L}u\left( \chi \right)=\int{_{_{\mathbb{R}}\mathbb{N}}\psi \left( u\left( x \right)-u\left( y \right) \right)J\left( x-y \right)dy}$of the type of the fractional p-Laplacian operator ...
Correa Ernesto, Pablo Arturo de
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An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces
Advances in Nonlinear Analysis, 2020 It is known that functions in a Sobolev space with critical exponent embed into the space of functions of bounded mean oscillation, and therefore satisfy the John-Nirenberg inequality and a corresponding exponential integrability estimate.
Martínez Ángel D., Spector Daniel
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The concentration-compactness principles for Ws,p(·,·)(ℝN) and application
Advances in Nonlinear Analysis, 2020 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 ...
Ho Ky, Kim Yun-Ho
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On functional reproducing kernels
Open Mathematics, 2023 We show that even if a Hilbert space does not admit a reproducing kernel, there could still be a kernel function that realizes the Riesz representation map.
Zhou Weiqi
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Sobolev extension in a simple case
Advanced Nonlinear StudiesIn this paper, we establish the existence of a bounded, linear extension operator T:L2,p(E)→L2,p(R2) $T :{L}^{2,p}\left(E\right)\to {L}^{2,p}\left({\mathbb{R}}^{2}\right)$ when 1 < p < 2 and E is a finite subset of R2 ${\mathbb{R}}^{2}$ contained in a ...
Drake Marjorie +3 more
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Open Mathematics, 2023 We deal with multiplicity of solutions to the following Schrödinger-Poisson-type system in this article: ΔHu−μ1ϕ1u=∣u∣2u+Fu(ξ,u,v),inΩ,−ΔHv+μ2ϕ2v=∣v∣2v+Fv(ξ,u,v),inΩ,−ΔHϕ1=u2,−ΔHϕ2=v2,inΩ,ϕ1=ϕ2=u=v=0,on∂Ω,\left\{\begin{array}{ll}{\Delta }_{H}u-{\mu }_{1}{
Li Shiqi, Song Yueqiang
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