890 citations · 3k across the 39 of their papers we have counts for
38 papers · 1 filter
Ground states of a nonlocal variational problem and Thomas-Fermi limit for the Choquard equation
Damiano Greco, Yanghong Huang, Zeng Liu +1
We study nonnegative optimizers of a Gagliardo-Nirenberg type inequality $$\iint_{\mathbb{R}^N \times \mathbb{R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-α}} dx\, dy\le C\Big(\int_{…
On the Phragmén-Lindelöf and the superposition principles for the -Laplacian
Pier Domenico Lamberti, Vitaly Moroz
We study sub and supersolutions for the -Laplace type elliptic equation of the form where is a radially symmetric domain in ${\ma…
Asymptotic profiles of ground state solutions for Choquard equations with a general local perturbation
Shiwang Ma, Vitaly Moroz
In this paper, we study the asymptotic behavior of ground state solutions for the nonlinear Choquard equation with a general local perturbation $$ -Δu+\varepsilon u=(I_α\ast |u|^{p…
Normalised solutions and limit profiles of the defocusing Gross-Pitaevskii-Poisson equation
Riccardo Molle, Vitaly Moroz, Giuseppe Riey
We study normalised solutions of the stationary Gross-Pitaevskii-Poisson (GPP) equation with a defocusing local nonlinear term, $$-Δu+λu+|u|^2u =(I_α*|u|^2)u\quad\text{in $\mathbb…
Thomas-Fermi theory of out-of-plane charge screening in graphene
Vitaly Moroz, Cyrill B. Muratov
This paper provides a variational treatment of the effect of external charges on the free charges in an infinite free-standing graphene sheet within the Thomas-Fermi theory. We est…
Asymptotic profiles for Choquard equations with combined attractive nonlinearities
Shiwang Ma, Vitaly Moroz
We study asymptotic behaviour of positive ground state solutions of the nonlinear Choquard equation $$ -Δu+\varepsilon u=(I_α\ast |u|^{p})|u|^{p-2}u+ |u|^{q-2}u \quad {\rm in} \ \m…
Asymptotic profiles for a nonlinear Kirchhoff equation with combined powers nonlinearity
Shiwang Ma, Vitaly Moroz
We study asymptotic behavior of positive ground state solutions of the nonlinear Kirchhoff equation $$ -\Big(a+b\int_{\mathbb R^N}|\nabla u|^2\Big)Δu+ λu= u^{q-1}+ u^{p-1} \quad {\…
Construction of infinitely many solutions for a critical Choquard equation via local Pohožaev identities
Fashun Gao, Vitaly Moroz, Minbo Yang +1
In this paper, we study a class of the critical Choquard equations with axisymmetric potentials, $$ -Δu+ V(|x'|,x'')u =\Big(|x|^{-4}\ast |u|^{2}\Big)u\hspace{4.14mm}\mbox{in}\hspac…
Asymptotic profile of ground states for the Schrödinger-Poisson-Slater equation
Zeng Liu, Vitaly Moroz
We study the Schrödinger-Poisson-Slater equation where and . By using direct variational analy…
Asymptotic profiles for a nonlinear Schrödinger equation with critical combined powers nonlinearity
Shiwang Ma, Vitaly Moroz
We study asymptotic behaviour of positive ground state solutions of the nonlinear Schrödinger equation where $N\ge…
Limit profiles for singularly perturbed Choquard equations with local repulsion
Zeng Liu, Vitaly Moroz
We study Choquard type equation of the form where , …
Nonlinear Inequalities with Double Riesz Potentials
Marius Ghergu, Zeng Liu, Yasuhito Miyamoto +1
We investigate the nonnegative solutions to the nonlinear integral inequality a.e. in , where , and…
Polyharmonic inequalities with nonlocal terms
Marius Ghergu, Yasuhito Miyamoto, Vitaly Moroz
We study the existence and non-existence of classical solutions for inequalities of type $$ \pm Δ^m u \geq \big(Ψ(|x|)*u^p\big)u^q \quad\mbox{ in } {\mathbb R}^N (N\geq 1). $$ Here…
High energy positive solutions for a coupled Hartree system with Hardy-Littlewood-Sobolev critical exponents
Fashun Gao, Haidong Liu, Vitaly Moroz +1
We study the coupled Hartree system $$ \left\{\begin{array}{ll} -Δu+ V_1(x)u =α_1\big(|x|^{-4}\ast u^{2}\big)u+β\big(|x|^{-4}\ast v^{2}\big)u &\mbox{in}\ \mathbb{R}^N,\\[1mm] -Δv+…
Gelfand problem on a large spherical cap
Yoshitsugu Kabeya, Vitaly Moroz
We study the behaviour of the minimal solution to the Gelfand problem on a spherical cap under the Dirichlet boundary conditions. The asymptotic behaviour of the solution is discus…
Gelfand-type problem for turbulent jets
Peter V. Gordon, Vitaly Moroz, Fedor Nazarov
We consider the model of auto-ignition (thermal explosion) of a free round reactive turbulent jet. This model falls into the general class of Gelfand-type problems and constitutes…
Groundstate asymptotics for a class of singularly perturbed -Laplacian problems in
Wedad Albalawi, Carlo Mercuri, Vitaly Moroz
We study the asymptotic behavior of positive groundstate solutions to the quasilinear elliptic equation \begin{equation} -Δ_{p} u + \varepsilon u^{p-1} - u^{q-1} +u^{\mathit{l}-1}…
A guide to the Choquard equation
Vitaly Moroz, Jean Van Schaftingen
We survey old and recent results dealing with the existence and properties of solutions to the Choquard type equations $$ -Δu + V(x)u = \bigl(|x|^{-(N-α)} * |u|^p\bigr)|u|^{p - 2}…
Boundary singularities of solutions of semilinear elliptic equations in the half-space with a Hardy potential
Catherine Bandle, Moshe Marcus, Vitaly Moroz
We study a nonlinear equation in the half-space with a Hardy potential, specifically \[-Δu -\fracμ{x_1^2}u+u^p=0\quad\text{in}\quad \mathbb R^n_+,\] where and $-\…
Least action nodal solutions for the quadratic Choquard equation
Marco Ghimenti, Vitaly Moroz, Jean Van Schaftingen
We prove the existence of a minimal action nodal solution for the quadratic Choquard equation where is…
Groundstates and radial solutions to nonlinear Schrödinger-Poisson-Slater equations at the critical frequency
Carlo Mercuri, Vitaly Moroz, Jean Van Schaftingen
We study the nonlocal Schrödinger-Poisson-Slater type equation where , ,…
Groundstates of nonlinear Choquard equations: Hardy-Littlewood-Sobolev critical exponent
Vitaly Moroz, Jean Van Schaftingen
We consider nonlinear Choquard equation $$ - Δu + V u = \bigl(I_α\ast |u|^{\fracα{N}+1}\bigr) |u|^{\fracα{N}-1} u\quad\text{in (\mathbb{R}^N)},$$ where , $V \in L^\infty (…
Limiting Bourgain-Brezis estimates for systems: theme and variations
Jean Van Schaftingen
J. Bourgain and H. Brezis have obtained in 2002 some new and surprising estimates for systems of linear differential equations, dealing with the endpoint case of sin…
Gelfand type problem for two phase porous media
Peter V. Gordon, Vitaly Moroz
We consider a generalization of the Gelfand problem arising in Frank-Kamenetskii theory of thermal explosion. This generalization is a natural extension of the Gelfand problem to t…