Results 61 to 70 of about 648,405 (147)

Well-posedness of Cauchy problem of fractional drift diffusion system in non-critical spaces with power-law nonlinearity

Advances in Nonlinear Analysis
In this article, we consider the global and local well-posedness of the mild solutions to the Cauchy problem of fractional drift diffusion system with higher-order nonlinearity. The main difficulty comes from the higher-order nonlinearity. Instead of the
Gu Caihong, Tang Yanbin
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Existence of ground state solutions for a class of Choquard equations with local nonlinear perturbation and variable potential

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, Luboš Pick, Daniel Spector   +2 more
wiley   +1 more source

Bifurcation results for the critical Choquard problem involving fractional p-Laplacian operator

Boundary Value Problems, 2018
By using an abstract critical point theorem based on a pseudo-index related to the cohomological index, we prove the bifurcation results for the critical Choquard problems involving fractional p-Laplacian operator: (−Δ)psu=λ|u|p−2u+(∫Ω|u|pμ,s∗|x−y|μdy)|u|
Yuling Wang, Yang Yang
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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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Sobolev and quasiconformal distortion of intermediate dimension with applications to conformal dimension

Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.
Abstract We study the distortion of intermediate dimension under supercritical Sobolev mappings and also under quasiconformal or quasisymmetric homeomorphisms. In particular, we extend to the setting of intermediate dimensions both the Gehring–Väisälä theorem on dilatation‐dependent quasiconformal distortion of dimension and Kovalev's theorem on the ...
Jonathan M. Fraser, Jeremy T. Tyson
wiley   +1 more source

Stability Results for Higher Order Solutions of Damped Wave Equations With Generalized Hartree‐Type Nonlinearity in Rn

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
In this paper, we investigate the dynamics of higher‐order solutions for a class of damped wave equations posed in Rn and driven by a nonlocal cubic convolution source of Hartree type. The model incorporates a higher order Laplacian of order σ, spatially dependent density functions, and frictional damping mechanisms.
Khaled Zennir, Keltoum Bouhali, Amal Alhujaylan, Abdelfateh Beghriche, Huaiqin Wu   +4 more
wiley   +1 more source

The Limiting Cases of Affine Hardy-Littlewood-Sobolev Inequalities

Axioms
In this paper, we studied the limiting cases of $\alpha \to n^-$ and $\alpha \to 0^+$ in the affine Hardy-Littlewood-Sobolev (HLS) inequalities proved in [25]. To be specific, we established affine logarithmic HLS inequalities and affine Beckner-type logarithmic Sobolev inequalities with respect to two different functions.
Youjiang Lin, Jiaming Lan, Jinghong Zhou
openaire   +1 more source

On the stability of critical points of the Hardy-Littlewood-Sobolev inequality

, 2023
This paper is concerned with the quantitative stability of critical points of the Hardy-Littlewood-Sobolev inequality. Namely, we give quantitative estimates for the Choquard equation: $$-Δu=(I_μ\ast|u|^{2_μ^*}) u^{2_μ^*-1}\ \ \text{in}\ \ \R^N,$$ where $u>0,\ N\geq 3,\ μ\in(0,N)$, $I_μ$ is the Riesz potential and $2_μ^* \coloneqq \frac{2N-μ}{N-2 ...
Liu, Kuan, Zhang, Qian, Zou, Wenming
openaire   +2 more sources

On the p-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity

Demonstratio Mathematica
In this article, we deal with the following pp-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity: M([u]s,Ap)(−Δ)p,Asu+V(x)∣u∣p−2u=λ∫RN∣u∣pμ,s*∣x−y∣μdy∣u∣pμ,s*−2u+k∣u∣q−2u,x∈RN,M({\left[u]}
Zhao Min, Song Yueqiang, Repovš Dušan D.   +2 more
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