Results 51 to 60 of about 6,369 (172)

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

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
doaj   +1 more source

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

Global existence and extinction for a fast diffusion p-Laplace equation with logarithmic nonlinearity and special medium void

Open Mathematics
This 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
doaj   +1 more source

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
doaj   +1 more source

Normalized solutions of the critical Schrödinger–Bopp–Podolsky system with logarithmic nonlinearity

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract In this paper, we study the following critical Schrödinger–Bopp–Podolsky system driven by the p$p$‐Laplace operator and a logarithmic nonlinearity: −Δpu+V(εx)|u|p−2u+κϕu=λ|u|p−2u+ϑ|u|p−2ulog|u|p+|u|p*−2uinR3,−Δϕ+a2Δ2ϕ=4π2u2inR3.$$\begin{equation*} {\begin{cases} -\Delta _p u+\mathcal {V}(\varepsilon x)|u|^{p-2}u+\kappa \phi u=\lambda |u|^{p-2 ...
Sihua Liang, Xueqi Sun, Shuaishuai Liang, Vicenţiu D. Rădulescu   +3 more
wiley   +1 more source

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
doaj  

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
doaj   +1 more source

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
doaj   +1 more source

Groundstates for a local nonlinear perturbation of the Choquard equations with lower critical exponent

, 2017
We prove the existence of ground state solutions by variational methods to the nonlinear Choquard equations with a nonlinear perturbation \[ -{\Delta}u+ u=\big(I_\alpha*|u|^{\frac{\alpha}{N}+1}\big)|u|^{\frac{\alpha}{N}-1}u+f(x,u)\qquad \text{ in ...
Van Schaftingen, Jean, Xia, Jiankang
core   +1 more source