Self-gravitating quantum matter may exist in a wide range of cosmological and astrophysical settings from the very early universe through to present-day boson stars. Such arises number different theories, including Peccei-Quinn axion UltraLight (ULDM) or Fuzzy (FDM) dark scenarios. We consider dynamical evolution perturbations spherically symmetric soliton, ground state solution Schr\"{o}dinger...

We consider the fractional generalizations of the phase volume, volume element, and Poisson brackets. These generalizations lead us to the fractional analog of the phase space. We consider systems on this fractional phase space and fractional analogs of the Hamilton equations. The fractional generalization of the average value is suggested. The fractional analogs of the Bogoliubov hierarchy equ...

In this paper, we obtain the existence of positive critical point with least energy for a class functionals involving nonlocal and supercritical variable exponent nonlinearities by applying variational method approximation techniques. We apply our results to Schrödinger–Poisson type systems Kirchhoff equations exponent, respectively.

Abstract We study the following non-cooperative type singularly perturbed systems involving fractional Laplacian operator: $$ \textstyle\begin{cases} \varepsilon ^{2s}(-\Delta )^{s} u+a(x)u=g(v), &amp; \text{in } \mathbb{R}^{N}, \\ v+a(x)v=f(u), \end{cases} { <mml:mi...

We provide an algorithm and a publicly available code to numerically evolve multicomponent Schr\"{o}dinger-Poisson (SP) systems with SO($n$) symmetry, including attractive or repulsive self-interactions in addition gravity. Focusing on the case where SP system represents non-relativistic limit of massive vector field, non-gravitational (in particular spin-spin interactions) introduce complexiti...