Zobrazeno 1 - 10
of 152
pro vyhledávání: '"MOROZ, VITALY"'
We study nonnegative optimizers of a Gagliardo-Nirenberg type inequality $$\iint_{\mathbb{R}^N \times \mathbb{R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-\alpha}} dx\, dy\le C\Big(\int_{{\mathbb R}^N}|u|^2 dx\Big)^{p\theta} \Big(\int_{{\mathbb R}^N}|u
Externí odkaz:
http://arxiv.org/abs/2406.18472
Autor:
Lamberti, Pier Domenico, Moroz, Vitaly
We study sub and supersolutions for the $p$-Laplace type elliptic equation of the form $$-\Delta_p u-V|u|^{p-2}u=0\quad\text{in $\Omega$},$$ where $\Omega$ is a radially symmetric domain in ${\mathbb{R}}^N$ and $V(x)\ge 0$ is a continuous potential s
Externí odkaz:
http://arxiv.org/abs/2405.16705
Autor:
Ma, Shiwang, Moroz, Vitaly
In this paper, we study the asymptotic behavior of ground state solutions for the nonlinear Choquard equation with a general local perturbation $$ -\Delta u+\varepsilon u=(I_\alpha \ast |u|^{p})|u|^{p-2}u+ g(u), \quad {\rm in} \ \mathbb R^N, \eqno(P_
Externí odkaz:
http://arxiv.org/abs/2405.02877
We study normalised solutions of the stationary Gross-Pitaevskii-Poisson (GPP) equation with a defocusing local nonlinear term, $$-\Delta u+\lambda u+|u|^2u =(I_\alpha*|u|^2)u\quad\text{in $\mathbb R^3$},\qquad\int_{\mathbb R^3}u^2dx=\rho^2,$$ where
Externí odkaz:
http://arxiv.org/abs/2308.04527
Autor:
Moroz, Vitaly, Muratov, Cyrill B.
Publikováno v:
Proc. R. Soc. A 480, 20230570 (2024)
This paper provides a variational treatment of the effect of external charges on the free charges in an infinite free-standing graphene sheet within the Thomas-Fermi theory. We establish existence, uniqueness and regularity of the energy minimizers c
Externí odkaz:
http://arxiv.org/abs/2306.02103
Autor:
Ma, Shiwang, Moroz, Vitaly
We study asymptotic behaviour of positive ground state solutions of the nonlinear Choquard equation $$ -\Delta u+\varepsilon u=(I_\alpha \ast |u|^{p})|u|^{p-2}u+ |u|^{q-2}u \quad {\rm in} \ \mathbb R^N, $$ where $N\ge 3$ is an integer, $p\in [\frac{N
Externí odkaz:
http://arxiv.org/abs/2302.13727
Autor:
Ma, Shiwang, Moroz, Vitaly
We study asymptotic behavior of positive ground state solutions of the nonlinear Kirchhoff equation $$ -\Big(a+b\int_{\mathbb R^N}|\nabla u|^2\Big)\Delta u+ \lambda u= u^{q-1}+ u^{p-1} \quad {\rm in} \ \mathbb R^N, $$ as $\lambda\to 0$ and $\lambda\t
Externí odkaz:
http://arxiv.org/abs/2211.14895
In this paper, we study a class of the critical Choquard equations with axisymmetric potentials, $$ -\Delta u+ V(|x'|,x'')u =\Big(|x|^{-4}\ast |u|^{2}\Big)u\hspace{4.14mm}\mbox{in}\hspace{1.14mm} \mathbb{R}^6, $$ where $(x',x'')\in \mathbb{R}^2\times
Externí odkaz:
http://arxiv.org/abs/2206.14958
Autor:
Ma, Shiwang, Moroz, Vitaly
Publikováno v:
In Journal of Differential Equations 15 December 2024 412:613-689
Autor:
Liu, Zeng, Moroz, Vitaly
We study the Schr\"{o}dinger-Poisson-Slater equation $$-\Delta u + u+\lambda(I_{2}*|u|^2)u=|u|^{p-2}u\quad\text{in $\mathbb R^3$},$$ where $p\in (3,6)$ and $\lambda>0$. By using direct variational analysis based on the comparison of the ground state
Externí odkaz:
http://arxiv.org/abs/2201.00860