Acta Mathematicae Applicatae Sinica, English Series最新文献

In this paper we study the eigenvalue problems of Schrödinger equations with energy-dependent potential on a lasso graph, and obtain a new regularized trace for this class of differential operators.

In this paper, we studied a stochastic predator-prey model of two predators with stage structure. By constructing a suitable stochastic Lyapunov function, the condition of stationary distribution is verified, and we get the sufficient condition for the model to have ergodic stationary distribution. Then, by using the Itô’s formula for the model, the sufficient conditions for the extinction of the predator population are given. Finally, some examples and numerical simulations are illustrated to verify the theoretical results.

The link of (2+1)-dimensional Harry Dym equation with the modified Kadomtsev-Petviashvili equation by the reciprocal transformation is shown. With the help of Darboux transformation, exact solutions of the (2+1)-dimensional Harry Dym equation are constructed and represented in terms of Wronskians.

In this paper we consider a kind of predator-prey model named Holling-Tanner model. Firstly, we prove all solutions of this model to be bounded from above. Secondly, we find a positive invariant set of the model, and prove the existence of stable limit cycle in this invariant set by Poincaré-Bendixson theorem for the unstable equilibrium. Thirdly, we get the region of parameters in which the corresponding stable equilibrium are also globally asymptotically stable. Lastly, we give a bifurcation diagram and illustration with two limit cycles for special parameters through numerical simulation. By our knowledge, the invariant set constructed in this paper is better than that in the book written by Murray.

We consider a system of k-Hessian equations

where 1 ≤ k ≤ n (n ≥ 2), α₁, α₂ and β₁ are positive constants, B = {x ∈ ℝⁿ: ∣x∣ < 1}. By giving the complete classification for the constants α₁, α₂ and β₁ according to the value of k, some sharp conditions are obtained for the existence, uniqueness and nonexistence results of k-convex solutions to the above problem.

In this paper, we explore the existence of analytic solutions for an iterative functional equation of the form

that originates from Painlevé equations. By an invertible transformation, we study the analytic solutions of an auxiliary equation under three different cases, and obtain the invertible analytic solutions for the original equation.

Let G = (V, E) be a simple graph and ϕ: V(G) ⋃ E(G) → {1, 2, ⋯, k} be a proper total-k-coloring of G. Let f(v) = ϕ(v)Π_uv∈E(G)ϕ(uv). The coloring ϕ is neighbor product distinguishing if f(u) ≠ f(v) for each edge uv ∈ E(G). The neighbor product distinguishing total chromatic number of G, denoted by χ ^″_Π (G), is the smallest integer k such that G admits a k-neighbor product distinguishing total coloring. Li et al. conjectured that χ ^″_Π (G) ≤ Δ(G) + 3 for any graph with at least two vertices and confirmed the conjecture for K₄-minor free graph. In this paper, we prove that for a graph G with at least two vertices, (1) if mad ((G)<{60 over 17}), then χ ^″_Π (G) ≤ max{Δ + 2, 8}; (2) if mad ((G)<{8 over 3}), then χ ^″_Π (G) ≤ max{Δ + 2, 6}. Furthermore, by using the Combinatorial Nullstellensatz, we simplify their proof and show that χ ^″_Π (G) ≤ max{Δ(G) + 2, 6} for any K₄-minor free graph.

In this paper we prove vanishing viscosity limits of a coupled chemotaxis-fluid model in a bounded domain Ω ⊂ ℝ³. The proof is based on the Banach’s fixed point theorem and the L^p-energy method. In addition, the L^∞-estimates and gradient estimates of the heat equations also play a crucial role.

This paper is concerned with the non-isentropic compressible Navier-Stokes/Allen-Cahn equations with the diffusion interface, which is an important mathematical model in the numerical simulation of compressible immiscible two-phase flow. When the space-asymptotic states (v_±, u_±, θ_±) lie in the rarefaction curve of the Riemann problem of the compressible Euler equations, we prove that the time-asymptotic state of solutions to the 1-D Cauchy problem is the rarefaction wave, that is, the stability of the rarefaction wave, where the strength of the rarefaction wave is not required to be small. Moreover, we consider the general gases including ideal polytropic gas and allow the different space-asymptotic states χ_± for the concentration difference of the mixture fluids. The proof is mainly based on a basic energy method. By product, we give the proof of the uniqueness of the global solutions to the 1-D Cauchy problem.

In this paper, the existence, uniqueness and Strichartz type estimates to solutions of multipoint problem for abstract linear and nonlinear wave equations are obtained. The equation includes a linear operator A defined in a Hilbert space H. We obtain the existence, uniqueness regularity properties, and Strichartz type estimates to solutions of a wide class of wave equations which appear in the fields of elastic rod, hydro-dynamical process, plasma, materials science and physics, by choosing the space H and the operator A.