Results 51 to 60 of about 5,037 (196)
Boundary Value Problems, 2021 In this paper, we consider a class of Choquard equations with Hardy–Littlewood–Sobolev lower or upper critical exponent in the whole space R N $\mathbb{R}^{N}$ . We combine an argument of L. Jeanjean and H. Tanaka (see (Proc. Am. Math. Soc. 131:2399–2408,
Xiaowei Li, Feizhi Wang
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Function spaces for decoupling
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract We introduce new function spaces LW,sq,p(Rn)$\mathcal {L}_{W,s}^{q,p}(\mathbb {R}^{n})$ that yield a natural reformulation of the ℓqLp$\ell ^{q}L^{p}$ decoupling inequalities for the sphere and the light cone. These spaces are invariant under the Euclidean half‐wave propagators, but not under all Fourier integral operators unless p=q$p=q$, in ...
Andrew Hassell +3 more
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Existence of Solutions for Choquard Type Elliptic Problems with Doubly Critical Nonlinearities
Advanced Nonlinear Studies, 2021 In this article, we first study the existence of nontrivial solutions to the nonlocal elliptic problems in ℝN{\mathbb{R}^{N}} involving fractional Laplacians and the Hardy–Sobolev–Maz’ya potential.
Shen Yansheng
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Generalized quasi‐geostrophic equation in critical Lorentz–Besov spaces, based on maximal regularity
Mathematische Nachrichten, Volume 299, Issue 3, Page 637-660, March 2026.Abstract We consider the quasi‐geostrophic equation with its principal part (−Δ)α${(-\mathrm{\Delta})^{\alpha}}$ for α>1/2$\alpha >1/2$ in Rn$\mathbb {R}^n$ with n≥2$n \ge 2$. We show that for every initial data θ0∈Ḃr,q1−2α+nr$\theta _0 \in \dot{B}^{1-2\alpha + \frac{n}{r}}_{r, q}$ with 1
Hideo Kozono +2 more
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Open MathematicsThis article is devoted to the global existence and extinction behavior of the weak solution to a fast diffusion pp-Laplace equation with logarithmic nonlinearity and special medium void.
Liu Dengming, Chen Qi
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Boundary Value Problems, 2021 In this paper, we focus on the existence of solutions for the Choquard equation { − Δ u + V ( x ) u = ( I α ∗ | u | α N + 1 ) | u | α N − 1 u + λ | u | p − 2 u , x ∈ R N ; u ∈ H 1 ( R N ) , $$\begin{aligned} \textstyle\begin{cases} {-}\Delta {u}+V(x)u ...
Jing Zhang, Qiongfen Zhang
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Potential trace inequalities via a Calderón‐type theorem
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract In this paper, we develop a general theoretical tool for the establishment of the boundedness of notoriously difficult operators (such as potentials) on certain specific types of rearrangement‐invariant function spaces from analogous properties of operators that are easier to handle (such as fractional maximal operators).
Zdeněk Mihula +2 more
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Riesz Potential on the Heisenberg Group
Journal of Inequalities and Applications, 2011 The relation between Riesz potential and heat kernel on the Heisenberg group is studied. Moreover, the Hardy-Littlewood-Sobolev inequality is established.
Xiao Jinsen, He Jianxun
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Some properties of solutions for a nonlinear integral system
Journal of Inequalities and Applications, 2016 In this paper, a nonlinear integral system is considered in critical space. Some important properties of positive solutions such as symmetry, monotonicity, integrability, and asymptotic behaviors, are obtained.
Xiaoying Wang, Junjie Li, Jiankai Xu
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Infinitely many non-radial solutions for a Choquard equation
Advances in Nonlinear Analysis, 2022 In this article, we consider the non-linear Choquard equation −Δu+V(∣x∣)u=∫R3∣u(y)∣2∣x−y∣dyuinR3,-\Delta u+V\left(| x| )u=\left(\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}\frac{| u(y){| }^{2}}{| x-y| }{\rm{d}}y\right)u\hspace{1.0em}\hspace{0.1em}\text{in}\
Gao Fashun, Yang Minbo
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