Results 1 to 10 of about 648,388 (139)
Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains [PDF]
Journal of Inequalities and Applications, 2017 This paper is concerned with an explicit value of the embedding constant from W 1 , q ( Ω ) $W^{1,q}(\Omega)$ to L p ( Ω ) $L^{p}(\Omega)$ for a domain Ω ⊂ R N $\Omega\subset\mathbb{R}^{N}$ ( N ∈ N $N\in\mathbb{N}$ ), where 1 ≤ q ≤ p ≤ ∞ $1\leq q\leq p ...
Makoto Mizuguchi +3 more
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Nonlinear Choquard equations on hyperbolic space [PDF]
Opuscula Mathematica, 2022 In this paper, our purpose is to prove the existence results for the following nonlinear Choquard equation \[-\Delta_{\mathbb{B}^{N}}u=\int_{\mathbb{B}^N}\dfrac{|u(y)|^{p}}{|2\sinh\frac{\rho(T_y(x))}{2}|^\mu} dV_y \cdot |u|^{p-2}u +\lambda u\] on the ...
Haiyang He
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Solutions for nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities
Advances in Nonlinear Analysis, 2022 In this article, we aimed to study a class of nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities as well as critical Hardy nonlinearities in RN{{\mathbb{R}}}^{N}.
Tao Mengfei, Zhang Binlin
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Anisotropic Choquard problems with Stein–Weiss potential: nonlinear patterns and stationary waves
Comptes Rendus. Mathématique, 2021 Weighted inequality theory for fractional integrals is a relatively less known branch of calculus that offers remarkable opportunities to simulate interdisciplinary processes.
Zhang, Youpei +2 more
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Integral inequalities with an extended Poisson kernel and the existence of the extremals
Advanced Nonlinear Studies, 2023 In this article, we first apply the method of combining the interpolation theorem and weak-type estimate developed in Chen et al. to derive the Hardy-Littlewood-Sobolev inequality with an extended Poisson kernel.
Tao Chunxia, Wang Yike
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Ground states of coupled critical Choquard equations with weighted potentials [PDF]
Opuscula Mathematica, 2022 In this paper, we are concerned with the following coupled Choquard type system with weighted potentials \[\begin{cases} -\Delta u+V_{1}(x)u=\mu_{1}(I_{\alpha}\!\ast\![Q(x)|u|^{\frac{N+\alpha}{N}}])Q(x)|u|^{\frac{\alpha}{N}-1}u+\beta(I_{\alpha}\!\ast\![Q(
Gaili Zhu +3 more
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Advanced Nonlinear Studies, 2021 Through conformal map, isoperimetric inequalities are equivalent to the Hardy–Littlewood–Sobolev (HLS) inequalities involved with the Poisson-type kernel on the upper half space.
Tao Chunxia
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Ground state sign-changing solutions for critical Choquard equations with steep well potential
Electronic Journal of Qualitative Theory of Differential Equations, 2022 In this paper, we study sign-changing solution of the Choquard type equation \begin{align*} -\Delta u+\left(\lambda V(x)+1\right)u =\big(I_\alpha\ast|u|^{2_\alpha^*}\big)|u|^{2_\alpha^*-2}u +\mu|u|^{p-2}u\quad \mbox{in}\ \mathbb{R}^N, \end{align*} where
Yong-Yong Li, Gui-Dong Li, Chun-Lei Tang
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The minimizing problem involving $p$-Laplacian and Hardy–Littlewood–Sobolev upper critical exponent
Electronic Journal of Qualitative Theory of Differential Equations, 2018 In this paper, we study the minimizing problem $$ S_{p,1,\alpha,\mu}:= \inf_{u\in W^{1,p}(\mathbb{R}^{N})\setminus\{0\}} \frac{ \int_{\mathbb{R}^{N}}|\nabla u|^{p}\mathrm{d}x - \mu \int_{\mathbb{R}^{N}} \frac{|u|^{p}}{|x|^{p}} \mathrm{d}x} {\left( \int_{\
Yu Su, Haibo Chen
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Resistance Conditions and Applications
Analysis and Geometry in Metric Spaces, 2013 This paper studies analytic aspects of so-called resistance conditions on metric measure spaces with a doubling measure. These conditions are weaker than the usually assumed Poincaré inequality, but however, they are sufficiently strong to imply several ...
Kinnunen Juha, Silvestre Pilar
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