Acta Mathematica Sinica-English Series最新文献

In this paper, we describe the wall-crossing of the two-parameter K-moduli space of pairs (ℙ², aQ + bL), where Q is a plane quintic curve and L is a line.

In this paper, we provide a sufficient condition, in the case of 0 < p < 1, for the existence of solutions to the general L_p Minkowski problem for polytopes.

In this article, we continue to study Kähler metrics on line bundles over projective spaces to find complete Kähler metrics with positive holomorphic sectional curvatures with two very special properties. These two special kinds of examples were not able to be found in our earlier paper of the first author and Ms. Duan. And therefore, we give a further step toward a famous Yau conjecture with the method in the co-homogeneity one geometry.

In this article, we show that the universal covering of any complete normal Kähler space of constant holomorphic sectional curvature on the regular locus is exactly biholomorphic to one of the complex projective space, the complex Euclidean space or the complex Euclidean ball. Moreover, we also prove that in a normal Stein space any bounded domain with complete Bergman metric of constant holomorphic sectional curvature on the regular locus is necessarily biholomorphic to the complex Euclidean ball, by which we generalize the classical Lu Qi-Keng uniformization theorem to the singular setting.

In this paper, we investigate the existence of normalized solutions for a quasilinear elliptic problem as follows

where −Δ_p is the p-Laplace operator, 1 < p < N, N ≥ 3, ρ > 0 and λ > 0. f is a continuous function and satisfies some suitable conditions. Based on a Nehari–Pohozaev manifold, we show the existence of positive normalized solutions by using the minimization method.

In this paper, we study the existence and multiplicity of homoclinic solutions for a class of second-order Hamiltonian system: u″(t) − L(t)u(t) + ⊽V(t,u) = 0, where L(t) and V(t,u) are not periodic in t. First, we introduce the definition of index and establish the corresponding index theory. Then, by using the index theory and critical point theory, we prove our main results under the asymptotic quadratic conditions of the potential function.

In this paper we will be concerned with the problem

where V is a potential continuous and f: ℝ → ℝ is a superlinear continuous function with exponential subcritical or exponential critical growth. We use as a main tool the Nehari manifold method in order to show existence of nonnegative solutions and existence of nodal solutions. Our results complement the classical result of “Solutions for quasilinear Schrdinger equations via the Nehari method” due to Jia–Quan Liu, Ya–Qi Wang and Zhi-Qiang Wang in the sense that in this article we are considering nonlinearity of the exponential type.

Let {X_n}_n≥0 be a p-type (p ≥ 2) supercritical branching process with immigration and mean matrix M. Suppose that M is positively regular and ρ is the maximal eigenvalue of M with the corresponding left and right eigenvectors v and u. Let ρ > 1 and (Y_{n}=rho^{-n}left[{bf u}cdot{X}_{n}-{{{rho}^{n+1}-1} over {rho}-1}left({boldsymbol u} cdot {boldsymbol lambda}right)right]), where the vector λ denotes the mean immigration rate. In this paper, we will show that Y_n is a martingale and converges to an r.v. Y as n → ∞. We study the rates of convergence to 0 as n → ∞ of

for any ε > 0, i = 1,…,p, 1 = (1,…,1) and l ∈ ℝ^p, the p-dimensional Euclidean space. It is shown that under certain moment conditions, the first two decay geometrically, while conditionally on the event Y ≥ α (α > 0) supergeometrically. The decay rate of the last probability is always supergeometric under a finite moment generating function assumption.

We study the mean orbital pseudo-metric for Polish dynamical systems and its connections with properties of the space of invariant measures. We give equivalent conditions for when the set of invariant measures generated by periodic points is dense in the set of ergodic measures and the space of invariant measures. We also introduce the concept of asymptotic orbital average shadowing property and show that it implies that every non-empty compact connected subset of the space of invariant measures has a generic point.

In this paper, we introduce the spectral Einstein functional for perturbations of Dirac operators on manifolds with boundary. Furthermore, we provide the proof of the Dabrowski–Sitarz–Zalecki type theorems associated with the spectral Einstein functionals for perturbations of Dirac operators, particularly in the cases of on 4-dimensional manifolds with boundary.