Results 1 to 10 of about 138 (90)
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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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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Optimality of Serrin type extension criteria to the Navier-Stokes equations
Advances in Nonlinear Analysis, 2021 We prove that a strong solution u to the Navier-Stokes equations on (0, T) can be extended if either u ∈ Lθ(0, T; U˙∞,1/θ,∞−α$\begin{array}{} \displaystyle \dot{U}^{-\alpha}_{\infty,1/\theta,\infty} \end{array}$) for 2/θ + α = 1, 0 < α < 1 or u ∈ L2(0, T;
Farwig Reinhard, Kanamaru Ryo
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Advanced Nonlinear Studies, 2021 The concentration-compactness principle for the Trudinger–Moser-type inequality in the Euclidean space was established crucially relying on the Pólya–Szegő inequality which allows to adapt the symmetrization argument.
Li Jungang, Lu Guozhen, Zhu Maochun
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Regularity for commutators of the local multilinear fractional maximal operators
Advances in Nonlinear Analysis, 2020 In this paper we introduce and study the commutators of the local multilinear fractional maximal operators and a vector-valued function b⃗ = (b1, …, bm). Under the condition that each bi belongs to the first order Sobolev spaces, the bounds for the above
Zhang Xiao, Liu Feng
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Advanced Nonlinear Studies, 2023 Let II be a bounded interval of R{\mathbb{R}} and λ1(I){\lambda }_{1}\left(I) denote the first eigenvalue of the nonlocal operator (−Δ)14{(-\Delta )}^{\tfrac{1}{4}} with the Dirichlet boundary.
Chen Lu, Wang Bohan, Zhu Maochun
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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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Admissibility versus Ap-Conditions on Regular Trees
Analysis and Geometry in Metric Spaces, 2020 We show that the combination of doubling and (1, p)-Poincaré inequality is equivalent to a version of the Ap-condition on rooted K-ary trees.
Nguyen Khanh Ngoc, Wang Zhuang
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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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