数学季刊

魏丽阳, 李峰

2024, 39(3): 221-234. doi:10.13371/j.cnki.chin.q.j.m.2024.03.001

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The domination problem of graphs is an important issue in the field of graph theory. This paper mainly considers the Italian domination number of the strong product between two paths. By constructing recursive Italian dominating functions, the upper bound of its Italian domination number is obtained, and then a partition method is proposed to prove its lower bound. Finally, this paper yields a sharp bound for the Italian domination number of the strong product of paths.

一类高秩大规模 T-Stein 方程的分解 Smith 方法

李想, 余波, 汤琼

2024, 39(3): 235-249. doi:10.13371/j.cnki.chin.q.j.m.2024.03.002

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We introduce a factorized Smith method (FSM) for solving large-scale highranked J-Stein equations within the banded-plus-low-rank structure framework. To effectively reduce both computational complexity and storage requirements, we develop techniques including deflation and shift, partial truncation and compression, as well as redesign the residual computation and termination condition. Numerical examples demonstrate that the FSM outperforms the Smith method implemented with a hierarchical
HODLR structured toolkit in terms of CPU time.

带有非常数位势的非线性 Choquard 方程正规化基态解

李楠, 赵慧燕, 许丽萍

2024, 39(3): 250-261. doi:10.13371/j.cnki.chin.q.j.m.2024.03.003

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In this paper, we mainly focus on the following Choquard equation......

非齐次Riemann-Hilbert边值问题的求解

张雯雯, 李平润

2024, 39(3): 262-269. doi:10.13371/j.cnki.chin.q.j.m.2024.03.004

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This paper studies the non-homogeneous generalized Riemann-Hilbert (RH) problems involving two unknown functions. Using the uniformization theorem, such problems are transformed into the case of homogeneous type. By the theory of classical boundary value problems, we adopt a novel method to obtain the sectionally analytic solutions of problems in strip domains, and analyze the conditions of solvability and properties of solutions in various domains.

有关广义 (h,m)-预不变凸函数的Ostrowski型不等式及其应用

李然, 连铁艳

2024, 39(3): 270-287. doi:10.13371/j.cnki.chin.q.j.m.2024.03.005

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A new concept generalized (h,m)−preinvex function on Yang’s fractal sets is proposed. Some Ostrowski’s type inequalities with two parameters for generalized (h,m)−preinvex function are established, where three local fractional inequalities involving generalized midpoint type, trapezoid type and Simpson type are derived as consequences. Furthermore, as some applications, special means inequalities and numerical quadratures for local fractional integrals are discussed.

关于三调和函数的Weyl引理研究

郑润洁, 曾佳敏, 方益

2024, 39(3): 288-294. doi:10.13371/j.cnki.chin.q.j.m.2024.03.006

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In this paper, by choosing some appropriate test functions, we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.

Sobolev型分数阶微分方程的伪S-渐近 (ω,c)-周期解

毛行宁, 常永奎

2024, 39(3): 295-306. doi:10.13371/j.cnki.chin.q.j.m.2024.03.007

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In this paper, we firstly recall some basic results on pseudo S-asymptotically (ω,c)-periodic functions and Sobolev type fractional differential equation. We secondly investigate some existence of pseudo S-asymptotically (ω,c)-periodic solutions for a semilinear fractional differential equations of Sobolev type. We finally present a simple example.

涉及调和数的组合恒等式

陈玉磊, 郭东威

2024, 39(3): 307-314. doi:10.13371/j.cnki.chin.q.j.m.2024.03.008

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In this paper, we firstly establish a combinatorial identity with a free parameter x, and then by means of derivative operation, several summation formulae concerning classical and generalized harmonic numbers, as well as binomial coefficients are derived.

具有一般奇异项基尔霍夫型方程解的存在性

王继楠, 孙大为

2024, 39(3): 315-323. doi:10.13371/j.cnki.chin.q.j.m.2024.03.009

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We study the existence of solutions for Kirchhoff-type equations. Firstly, we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum. Then, we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation when λ is small enough.

关于KdV方程簇Tau函数仿射坐标的一个注记

付志鹏

2024, 39(3): 324-330. doi:10.13371/j.cnki.chin.q.j.m.2024.03.010

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We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy.

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