Existence and uniqueness of mild solutions of nonlinear difference-integrodifferential equation with nonlocal condition

In this paper we investigate the existence, uniqueness and continuous dependence of solutions of the difference-integrodifferential equations. The results are obtained by using the well known Banach fixed point theorem, the theory of semigroups and the inequality established by B. G. Pachpatte

Existence and uniqueness of solution of inhomogeneous semilinear evolution equation with nonlocal condition

In this paper, we study the existence and uniqueness of solution of inhomogeneous semilinear evolution equation with nonlocal condition in cone metric space. The result is obtained by using the some extensions of Banach's contraction principle in complete cone metric space

SARCS strong lensing galaxy groups: I - optical, weak lensing, and scaling laws

We present the weak lensing and optical analysis of the SL2S-ARCS (SARCS) sample of strong lens candidates. The sample is based on the Strong Lensing Legacy Survey (SL2S), a systematic search of strong lensing systems in the photometric Canada-France-Hawaii Telescope Legacy Survey (CFHTLS). The SARCS sample focuses on arc-like features and is designed to contain mostly galaxy groups. We briefly present the weak lensing methodology that we use to estimate the mass of the SARCS objects. Among 126 candidates, we obtain a weak lensing detection for 89 objects with velocity dispersions of the Singular Isothermal Sphere mass model ranging from 350 to 1000 km/s with an average value of 600km/s, corresponding to a rich galaxy group (or poor cluster). From the galaxies belonging to the bright end of the group's red sequence (M_i<-21), we derive the optical properties of the SARCS candidates. We obtain typical richnesses of N=5-15 galaxies and optical luminosities of L=0.5-1.5e+12 Lsol (within a radius of 0.5 Mpc). We use these galaxies to compute luminosity density maps, from which a morphological classification reveals that a large fraction of the sample are groups with a complex light distribution, either elliptical or multimodal, suggesting that these objects are dynamically young structures. We finally combine the lensing and optical analyses to draw a sample of 80 most secure group candidates, i.e. weak lensing detection and over-density at the lens position in the luminosity map, to remove false detections and galaxy-scale systems from the initial sample. We use this reduced sample to probe the optical scaling relations in combination with a sample of massive galaxy clusters. We detect the expected correlations over the probed range in mass with a typical scatter of 25% in the SIS velocity dispersion at a given richness or luminosity, making these scaling laws interesting mass proxie