Results 81 to 90 of about 1,216,221 (148)

Multiple solutions to a magnetic nonlinear Choquard equation

, 2012
We consider the stationary nonlinear magnetic Choquard equation, where A is a real-valued vector potential, V is a real-valued scalar potential, N ≥ 3, α ε (0,N)and 2 - (α/N) < p < (2N - α)/(N-2).
Secchi, S., CINGOLANI, Silvia, Clapp, M.
core   +2 more sources

The existence of positive ground state solutions for the Choquard type equation on groups of polynomial growth

, 2022
In this paper, let $G$ be a Cayley graph of a discrete group of polynomial growth with homogeneous dimension $N\geq3$. We study the Choquard type equation on $G$: \begin{equation} \Delta u+(R_{\alpha}\ast\mid u\mid^{p})\mid u\mid^{p-2}u=0, \end{equation}
Li, Ruowei
core  

Ground state of a magnetic nonlinear Choquard equation.

, 2019
We consider the stationary magnetic nonlinear Choquard equation −(∇ + iA(x))2u + V(x)u = (1|x|α ∗ (|u|) ) f(|u|) |u| u, where A : RN → RN is a vector potential, V is a scalar potential, f : R → R and F is the primitive of f .
Mamani, Guido Gutierrez, Bueno, Hamilton Prado, Pereira, Gilberto de Assis   +2 more
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Ground state solutions for asymptotically periodic fractional Choquard equations

Electronic Journal of Qualitative Theory of Differential Equations, 2019
This paper is dedicated to studying the following fractional Choquard equation \begin{equation*} (-\triangle)^s u+V(x)u=\left(\int_{\mathbb{R}^N}\frac{Q(y)F(u(y))}{|x-y|^\mu}\mathrm{d}y\right)Q(x)f(u), \qquad u\in H^s(\mathbb{R}^{N}), \end{equation*
Sitong Chen, Xianhua Tang
doaj   +1 more source

Local uniqueness of ground states for the generalized Choquard equation [PDF]

We consider the generalized Choquard equation of the type -Δ Q + Q = I(|Q|(p))|Q|(p-2)Q, for 3≤n≤5, with Q∈Hrad1(Rn), where the operator I is the classical Riesz potential defined by I(ƒ)(x)=(-Δ)−1ƒ(x) and the exponent p∈(2,1+4/(n-2)) is energy ...
George Venkov, Mirko Tarulli, Vladimir Georgiev   +2 more
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Existence, symmetry, and regularity of ground states of a nonlinear Choquard equation in the hyperbolic space

Advances in Nonlinear Analysis
In this study, we explore the positive solutions of a nonlinear Choquard equation involving the Green kernel of the fractional operator (−ΔBN)−α⁄2{\left(-{\Delta }_{{{\mathbb{B}}}^{N}})}^{-\alpha /2} in the hyperbolic space, where ΔBN{\Delta }_{{{\mathbb{
Gupta Diksha, Sreenadh Konijeti
doaj   +1 more source

Concentration phenomena for the fractional relativistic Schrödinger-Choquard equation [PDF]

We consider the fractional relativistic Schrödinger-Choquard equation (equation presented), where ε > 0 is a small parameter, s (0, 1), m > 0, N > 2s, μ (0, 2s), (-δ + m2)s is the fractional relativistic Schrödinger operator, V: RN → R is a ...
Ambrosio V.
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A priori estimates for a critical Schrodinger-Newton equation

Electronic Journal of Differential Equations, 2013
Under natural energy and decay assumptions, we derive a priori estimates for solutions of a Schrodinger-Newton type of equation with critical exponent.
Marcelo M. Disconzi
doaj  

The Choquard logarithmic equation involving a nonlinearity with exponential growth

, 2022
In the present work, we are concerned with the Choquard Logarithmic equation $-\Delta u + au + \lambda (\ln|\cdot|\ast |u|^{2})u = f(u)$ in $ \mathbb{R}^2$, for $ a> 0 $, $ \lambda > 0 $ and a nonlinearity $f$ with exponential critical growth. We prove

core  

Some existence and uniqueness results for logistic Choquard equation

, 2021
We consider the following doubly nonlocal nonlinear logistic problem driven by the fractional $p$-Laplacian \begin{equation*} \pl u = f(x,u) -\cq ~\text{in}~ \O, ~u=0 ~\text{in}~ \Rn\setminus\O.
Giacomoni, J., Sreenadh, K., Anthal, G. C.   +2 more
core   +1 more source