Results 1 to 10 of about 1,954 (101)
Steklov problems for the p−Laplace operator involving Lq-norm
Moroccan Journal of Pure and Applied Analysis, 2022 In this paper, we are concerned with the study of the spectrum for the nonlinear Steklov problem of the form {Δpu=|u|p-2uin Ω,|∇u|p-2∂u∂v=λ‖u‖q,∂Ωp-q|u|q-2uon ∂Ω,\left\{ {\matrix{{{\Delta _p}u = {{\left| u \right|}^{p - 2}}u} \hfill & {{\rm{in}}\,\Omega ,
Alaoui My Driss Morchid +2 more
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Weighted W1, p (·)-Regularity for Degenerate Elliptic Equations in Reifenberg Domains
Advances in Nonlinear Analysis, 2021 Let w be a Muckenhoupt A2(ℝn) weight and Ω a bounded Reifenberg flat domain in ℝn. Assume that p (·):Ω → (1, ∞) is a variable exponent satisfying the log-Hölder continuous condition.
Zhang Junqiang, Yang Dachun, Yang Sibei
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A Generalized Version of the Lions-Type Lemma
Annales Mathematicae Silesianae, 2023 In this short paper, I recall the history of dealing with the lack of compactness of a sequence in the case of an unbounded domain and prove the vanishing Lions-type result for a sequence of Lebesgue-measurable functions.
Chmara Magdalena
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Concentration-compactness principle associated with Adams' inequality in Lorentz-Sobolev space
Advanced Nonlinear Studies, 2022 The concentration-compactness principle of Lions type in Euclidean space relies on the Pólya-Szegö inequality, which is not available in non-Euclidean settings.
Li Dongliang, Zhu Maochun
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Moroccan Journal of Pure and Applied Analysis, 2023 We investigate the existence of non-trivial weak solutions for the following p(x)-Kirchhoff bi-nonlocal elliptic problem driven by both p(x)-Laplacian and p(x)-Biharmonic operators {M(σ)(Δp(x)2u-Δp(x)u)=λϑ(x)|u|q(x)-2u(∫Ωϑ(x)q(x)|u|q(x)dx)r in Ω,u∈W2,p(.)
Jennane Mohsine, Alaoui My Driss Morchid
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Advances in Nonlinear Analysis, 2023 In this article, we develop a new set of results based on a non-local gradient jointly inspired by the Riesz ss-fractional gradient and peridynamics, in the sense that its integration domain depends on a ball of radius δ>0\delta \gt 0 (horizon of ...
Bellido José Carlos +2 more
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Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, I [PDF]
, 2004 36 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.-- Part II of this paper published in: Approx. Theory Appl. 18(2): 1-32 (2002), available at: http://e-archivo.uc3m.es/handle/10016/6483MR#: MR2047389 (2005k:42062)Zbl#: Zbl 1081.42024In this ...
Pestana, Domingo +3 more
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Small perturbations of critical nonlocal equations with variable exponents
Demonstratio Mathematica, 2023 In this article, we are concerned with the following critical nonlocal equation with variable exponents: (−Δ)p(x,y)su=λf(x,u)+∣u∣q(x)−2uinΩ,u=0inRN\Ω,\left\{\begin{array}{ll}{\left(-\Delta )}_{p\left(x,y)}^{s}u=\lambda f\left(x,u)+{| u| }^{q\left(x)-2}u&
Tao Lulu, He Rui, Liang Sihua
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Trace Operators on Regular Trees
Analysis and Geometry in Metric Spaces, 2020 We consider different notions of boundary traces for functions in Sobolev spaces defined on regular trees and show that the almost everywhere existence of these traces is independent of the chosen definition of a trace.
Koskela Pekka +2 more
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Moroccan Journal of Pure and Applied Analysis, 2021 We prove in this paper some existence and unicity results of entropy and renormalized solutions for some nonlinear elliptic equations with general anisotropic diffusivities and variable exponents. The data are assumed to be merely integrable.
Moumni Mostafa El, Mohamed Deval Sidi
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