On some impulsive fractional differential equations in Banach spaces

This paper deals with some impulsive fractional differential equations in Banach spaces. Utilizing the Leray-Schauder fixed point theorem and the impulsive nonlinear singular version of the Gronwall inequality, the existence of $PC$-mild solutions for some fractional differential equations with impulses are obtained under some easily checked conditions. At last, an example is given for demonstration

Structure and morphology of X-ray selected AGN hosts at 1<z<3 in CANDELS-COSMOS field

We analyze morphologies of the host galaxies of 35 X-ray selected active galactic nucleus (AGNs) at $z\sim2$ in the Cosmic Evolution Survey (COSMOS) field using Hubble Space Telescope/WFC3 imaging taken from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS). We build a control sample of 350 galaxies in total, by selecting ten non-active galaxies drawn from the same field with the similar stellar mass and redshift for each AGN host. By performing two dimensional fitting with GALFIT on the surface brightness profile, we find that the distribution of S$\`e$rsic index (n) of AGN hosts does not show a statistical difference from that of the control sample. We measure the nonparametric morphological parameters (the asymmetry index A, the Gini coefficient G, the concentration index C and the M20 index) based on point source subtracted images. All the distributions of these morphological parameters of AGN hosts are consistent with those of the control sample. We finally investigate the fraction of distorted morphologies in both samples by visual classification. Only $\sim$15% of the AGN hosts have highly distorted morphologies, possibly due to a major merger or interaction. We find there is no significant difference in the distortion fractions between the AGN host sample and control sample. We conclude that the morphologies of X-ray selected AGN hosts are similar to those of nonactive galaxies and most AGN activity is not triggered by major merger.Comment: 5 pages, 3 figures, accepted for publication in The Astrophysical Journal Letter

On some existence results of mild solutions for nonlocal integrodifferential Cauchy problems in Banach spaces

In this paper, we study a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. Existence results of mild solutions are proved for a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. The main results are obtained by using the Schaefer fixed point theorem and semigroup theory. Finally, an example is given for demonstration