A fractional Kirchhoff problem involving a singular term and a critical nonlinearity [PDF]
Advances in Nonlinear Analysis, 2017 In this paper, we consider the following critical nonlocal problem:
Fiscella Alessio
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Advances in Nonlinear Analysis, 2023 In this article, we study the following general Kirchhoff type equation: −M∫R3∣∇u∣2dxΔu+u=a(x)f(u)inR3,-M\left(\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}| \nabla u{| }^{2}{\rm{d}}x\right)\Delta u+u=a\left(x)f\left(u)\hspace{1em}{\rm{in}}\hspace{0.33em}{{\
Zhang Jian, Liu Huize, Zuo Jiabin
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On Kac's principle of not feeling the boundary for the Kohn Laplacian on the Heisenberg group [PDF]
, 2015 In this note we construct an integral boundary condition for the Kohn Laplacian in a given domain on the Heisenberg group extending to the setting of the Heisenberg group M. Kac's "principle of not feeling the boundary".
Ruzhansky, Michael, Suragan, Durvudkhan
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Geometric maximizers of Schatten norms of some convolution type integral operators [PDF]
, 2017 In this paper we prove that the ball is a maximizer of the Schatten $p$-norm of some convolution type integral operators with non-increasing kernels among all domains of a given measure in $\mathbb R^{d}$.
Ruzhansky, Michael, Suragan, Durvudkhan
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Infinitely many solutions for non-local problems with broken symmetry
Advances in Nonlinear Analysis, 2018 The aim of this paper is to investigate the existence of solutions of the non-local elliptic ...
Bartolo Rossella +2 more
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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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Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity [PDF]
, 2014 This paper deals with the existence and the asymptotic behavior of non-negative solutions for a class of stationary Kirchhoff problems driven by a fractional integro-differential operator $\mathcal L_K$ and involving a critical nonlinearity.
Autuori, Giuseppina +2 more
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A note on semilinear fractional elliptic equation: analysis and discretization [PDF]
, 2016 In this paper we study existence, regularity, and approximation of solution to a fractional semilinear elliptic equation of order $s \in (0,1)$. We identify minimal conditions on the nonlinear term and the source which leads to existence of weak ...
Antil, Harbir +2 more
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Very large solutions for the fractional Laplacian: Towards a fractional Keller–Osserman condition
Advances in Nonlinear Analysis, 2017 We look for solutions of (-△)su+f(u)=0{{\left(-\triangle\right)}^{s}u+f(u)=0} in a bounded smooth domain Ω, s∈(0,1){s\in(0,1)}, with a strong singularity at the boundary. In particular, we are interested in solutions which are L1(Ω){L^{1}(\Omega)} and
Abatangelo Nicola
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Sobolev spaces with non-Muckenhoupt weights, fractional elliptic operators, and applications [PDF]
, 2018 We propose a new variational model in weighted Sobolev spaces with non-standard weights and applications to image processing. We show that these weights are, in general, not of Muckenhoupt type and therefore the classical analysis tools may not apply ...
Antil, Harbir, Rautenberg, Carlos N.
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