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Ground state solutions for nonlinearly coupled systems of Choquard type with lower critical exponent

Electronic Journal of Qualitative Theory of Differential Equations, 2020
In this paper, we study the existence of ground state solutions for the following nonlinearly coupled systems of Choquard type with lower critical exponent by variational methods \begin{equation*} \begin{cases} \displaystyle-\Delta u+V(x)u=(I_\alpha\ast ...
Anran Li, Peiting Wang, Chongqing Wei
doaj   +1 more source

On the stability of a version of nonlocal Sobolev inequality

Bulletin of Mathematical Sciences
In this paper, we investigate the stability of the corresponding nonlocal Sobolev inequality ∫ℝN|Δu|2dx≥S∗∫ℝN(|x|−α∗|u|p)updx1p,∀u∈𝒟2,2(ℝN), where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] is the best constant.
Weiwei Ye, Xinyun Zhang
doaj   +1 more source

Mizohata–Takeuchi inequalities for orthonormal systems

Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.
Abstract We establish some weighted L2$L^2$ inequalities for Fourier extension operators in the setting of orthonormal systems. In the process, we develop a direct approach to such inequalities based on generalized Wigner distributions, complementing the Schatten space approach that is prevalent in the wider context of estimates for such orthonormal ...
Jonathan Bennett, Neal Bez, Susana Gutiérrez, Shohei Nakamura, Itamar Oliveira   +4 more
wiley   +1 more source

A weighted Hardy-Sobolev-Maz’ya inequality [PDF]

, 2014
We provide a weighted extension of a Hardy-Sobolev-Maz’ya inequality that is due to Filippas, Maz’ya and ...
Sourdis, Christos
core  

Solutions with prescribed mass for a critical Choquard equation driven by a local-nonlocal operator [PDF]

Opuscula Mathematica
In this paper, we study the normalized solutions of the following critical growth Choquard equation with mixed local and nonlocal operators: \[\begin{split}-\Delta u +(-\Delta)^s u &= \lambda u +\mu |u|^{p-2}u +(I_{\alpha}*|u|^{2^*_{\alpha}})|u|^{2^*_ ...
Nidhi Nidhi, Konijeti Sreenadh
doaj   +1 more source

Existence of Weak Solutions for the Equations of a Non‐Newtonian Fluid With Non‐Standard Growth

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 106, Issue 7, July 2026.
ABSTRACT We consider the equations of a non‐Newtonian incompressible fluid in a general time‐space cylinder ΩT=Ω×(0,T)⊂Rn×R,n≥2$\Omega _{T} = \Omega \times (0,T) \subset \mathbb {R}^{n} \times \mathbb {R}, n \ge 2$. We assume that the rheology of the fluid is changing with respect to time and space, and satisfies, for each (x,t)∈ΩT$(x,t) \in \Omega _{T}
Hyeong‐Ohk Bae, Jörg Wolf
wiley   +1 more source

The best constant in a weighted Hardy-Littlewood-Sobolev inequality [PDF]

Proceedings of the American Mathematical Society, 2007
We prove the uniqueness for the solutions of the singular nonlinear PDE system: (1)
Chen, Wenxiong, Li, Congming
openaire   +2 more sources

Long‐Time Solvability and Asymptotics for the 3D Rotating MHD Equations

Mathematische Nachrichten, Volume 299, Issue 6, Page 1480-1509, June 2026.
ABSTRACT We consider the initial value problem for the 3D incompressible rotating MHD equations around a constant magnetic field. We prove the long‐time existence and uniqueness of solutions for small viscosity coefficient and high rotating speed. Moreover, we investigate the asymptotic behavior of solutions in the limit of vanishing viscosity and fast
Hiroki Ohyama
wiley   +1 more source

A strong quantitative form of the fractional isoperimetric inequality

Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.
Abstract We show a strong version of the fractional quantitative isoperimetric inequality, in which the isoperimetric deficit controls not only the Fraenkel asymmetry but also a sort of oscillation of the boundary. This generalizes the local result by Fusco and Julin in [22].
Eleonora Cinti, Enzo Maria Merlino, Berardo Ruffini   +2 more
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