This work searches for the candidates of Galactic disk star clusters in Gaia Early Data Release 3 (Gaia EDR3) and determines their basic parameters from color–magnitude diagrams (CMDs). A friends-of-friends method for membership determination and stellar population models including binary stars (ASPS) and rotating stars are adopted. As a result, 868 new star cluster candidates are found, besides 2729 known ones. When checking the CMD of each candidate, 61 new candidates show main sequences including a turnoff, which suggests that they are real star clusters. The basic parameters, including distance modulus, color excess, metallicity, age (or age range), primordial binary fraction, and rotating star fraction, are determined carefully by fitting the morphologies of CMDs of 61 newly identified star clusters and 594 known star clusters, which have relatively clear main sequences. The CMDs are fitted in considerable detail to ensure the reliability of property parameters of clusters. All final results are included in a new star cluster catalog, which is named LI team’s Star Cluster (LISC), and the catalog is available in the Zenodo repository.

No abstract

Reliable fundamental parameters of star clusters such as distance modulus, metallicity, age, extinction, and binary fraction are of key importance for astrophysical studies. Although a lot of new star clusters were identified from the data of, e.g., Gaia Data Release 2 (Gaia DR2), the fundamental parameters of many clusters were not determined reliably. This work makes use of the photometry data of Gaia DR2 and a good color–magnitude diagram (CMD) analysis tool, Powerful CMD, to determine the fundamental parameters of 49 new star clusters in detail. All CMDs are fitted carefully by both statistics and by eye, to make sure the CMDs are reproduced as well as possible. As a result, the fundamental parameters of 22 clusters are determined reliably, and those of the others are also determined as well as we can. Because the width of the main sequence in the color direction is used, combined with other widely used CMD features to constrain the fundamental parameters, the results of this work are more reliable than those reported by single-star isochrone fits. As a feature of this work, the primordial binary fractions and rotating star fractions of star clusters have been reported, which are useful for many works, in particular for some simulation research.

We consider the following nonlinear fractional Schrödinger equation: $$ (-\triangle )^{s} u+V(x)u=g(u) \quad \text{in } \mathbb{R} ^{N}, $$ ( − △ ) s u + V ( x ) u = g ( u ) in  R N , where $s\in (0, 1)$ s ∈ ( 0 , 1 ) , $N>2s$ N > 2 s , $V(x)$ V ( x ) is differentiable, and $g\in C ^{1}(\mathbb{R} , \mathbb{R} )$ g ∈ C 1 ( R , R ) . By exploiting the minimization method with a constraint over Pohoz̆aev manifold, we obtain the existence of ground state solutions. With the help of Pohoz̆aev identity we also process the existence of the least energy solutions for the above equation. Our results improve the existing study on this nonlocal problem with Berestycki–Lions type nonlinearity to the one that does not need the oddness assumption.

This paper is dedicated to studying the following Kirchhoff-type problem: $$ \textstyle\begin{cases} -m ( \Vert \nabla u \Vert ^{2}_{L^{2}(\mathbb{R} ^{N})} )\Delta u+V(x)u=f(u), & x\in \mathbb{R} ^{N}; \\ u\in H^{1}(\mathbb{R} ^{N}), \end{cases} $$ { − m ( ∥ ∇ u ∥ L 2 ( R N ) 2 ) Δ u + V ( x ) u = f ( u ) , x ∈ R N ; u ∈ H 1 ( R N ) , where $N=1,2$ N = 1 , 2 , $m:[0,\infty )\rightarrow (0,\infty )$ m : [ 0 , ∞ ) → ( 0 , ∞ ) is a continuous function, $V:\mathbb{R} ^{N}\rightarrow \mathbb{R} $ V : R N → R is differentiable, and $f\in \mathcal{C}(\mathbb{R} ,\mathbb{R} )$ f ∈ C ( R , R ) . We obtain the existence of a ground state solution of Nehari–Pohozaev type and the least energy solution under some assumptions on V, m, and f. Especially, the existence of nonlocal term $m(\|\nabla u\|^{2}_{L^{2}(\mathbb{R} ^{N})})$ m ( ∥ ∇ u ∥ L 2 ( R N ) 2 ) and the lack of Hardy’s inequality and Sobolev’s inequality in low dimension make the problem more complicated. To overcome the above-mentioned difficulties, some new energy inequalities and subtle analyses are introduced.