Results 61 to 70 of about 1,494,768 (123)

Normalized solutions for a fractional Choquard-type equation with exponential critical growth in $\mathbb{R}$ [PDF]

, 2023
In this paper, we study the following fractional Choquard-type equation with prescribed mass \begin{align*} \begin{cases} (-\Delta)^{1/2}u=\lambda u +(I_\mu*F(u))f(u),\ \ \mbox{in}\ \mathbb{R}, \displaystyle\int_{\mathbb{R}}|u|^2 \mathrm{d}x=a^2,
Sun, Qian, Chen, Wenjing, Wang, Zexi
core   +1 more source

Concentration phenomena for anisotropic fractional Choquard equations and potential competition

Bulletin of Mathematical Sciences
In this paper, we study the existence of a weak solution to the following anisotropic fractional Choquard equation in [Formula: see text] as follows: ∑i=1m(−Δ)pisv+∑i=1mV(ζx)|v|pi−2v=λ1|x|μ∗Q(ζy)F(v)Q(ζx)𝔣(v)+(v+)qs∗−2v+,v+(x)=max{v(x),0}, where [Formula:
Trang Quynh Pham, Thin Van Nguyen
doaj   +1 more source

Applications of the Fractional Calculus: On a Discretization of Fractional Diffusion Equation in One Dimension

, 2010
The paper discusses the problem of classical and fractional diffusion models. It is known that the classical model fails in heterogeneous structures with locations where particles move at a large speed over a long distance.
Tomas Kisela
core   +1 more source

Critical Fractional Choquard–Kirchhoff Equation with p-Laplacian and Perturbation Terms on the Heisenberg Group

Fractal and Fractional
In this paper, we are interested in a class of critical fractional Choquard–Kirchhoff equations with p-Laplacian on the Heisenberg group. By employing several critical point theorems, we obtain the existence and multiplicity of nontrivial solutions under
Xueyan Ma, Sihua Liang, Yueqiang Song
doaj   +1 more source

On fractional Choquard equations

, 2015
We investigate a class of nonlinear Schrodinger equations with a generalized Choquard nonlinearity and fractional diffusion.
Gaetano Siciliano, SQUASSINA, Marco, Pietro d'Avenia   +2 more
core  

Optimal control of fractional systems: a diffusive formulation [PDF]

, 2010
Optimal control of fractional linear systems on a finite horizon can be classically formulated using the adjoint system. But the adjoint of a causal fractional integral or derivative operator happens to be an anti-causal operator: hence, the adjoint ...
Matignon, Denis
core  

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  

A design methodology to enable sampling PLLs to synthesise fractional-N frequencies [PDF]

, 2011
A novel design methodology is proposed to enable sampling phase-locked loops (SPLL) to synthesise fractional-N frequencies. To date, SPLL can only generate integer-N frequencies.
Xu, Tao, Condon, Marissa, Linigyong, Shen   +2 more
core   +1 more source

On Uniqueness for the Generalized Choquard Equation

, 2020
We consider the generalized Choquard equation describing trapped electron gas in three dimensional case. The study of orbital stability of the energy minimizers (known as ground states) depends essentially in the local uniqueness of these minimizers. The
George Venkov, Vladimir Georgiev, Georgiev V., Venkov G.   +3 more
core   +1 more source

Infinitely many free or prescribed mass solutions for fractional Hartree equations and Pohozaev identities

Advanced Nonlinear Studies
In this paper we study the following nonlinear fractional Hartree (or Choquard-Pekar) equation (−Δ)su+μu=(Iα*F(u))F′(u) inRN, ${\left(-{\Delta}\right)}^{s}u+\mu u=\left({I}_{\alpha }{\ast}F\left(u\right)\right){F}^{\prime }\left(u\right)\quad \text{in} {\
Cingolani Silvia, Gallo Marco, Tanaka Kazunaga   +2 more
doaj   +1 more source