Pure Mathematics

Journal Information
ISSN / EISSN : 2160-7583 / 2160-7605
Published by: Hans Publishers (10.12677)
Total articles ≅ 977
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婧李 雯
Published: 1 January 2021
Pure Mathematics, Volume 11, pp 1048-1054; https://doi.org/10.12677/pm.2021.116118

Abstract:
本文运用Leray-Schauder二择一定理,研究了一类分数阶微分方程的三点边值问题 得到该问题解的存在性。进一步证明了限制非线性项的函数k(t),在被形如Btμ的函数控制后,该问题至少存在一个解。最后,通过实例验证了结论的有效性。 In this paper, three-point boundary value problem for a class of fractional differential equations are studied by using Leray-Schauder nonlinear alternative. The existence of the solution is obtained. Furthermore, it is proved that the function k(t), which is limited to the nonlinear term, exists at least one solution of the problem when it is controlled by a function of the form Btμ. Finally, an example is given to verify the validity of the conclusion.
玉余 荣
Published: 1 January 2021
Pure Mathematics, Volume 11, pp 1031-1047; https://doi.org/10.12677/pm.2021.116117

Abstract:
本文针对五阶偏微分方程提出了时间多区域时空谱方法. 该方法在空间方向上采用 Legendre-Petrov-Galerkin 方法, 在时间方向上采用多区域的 Legendre-tau 方法, 即: 把时间区间分成多个区域, 并在每个区域上采用 Legendre-tau 方法. 同时, 本文给出了该方法在线性问题上的误差分析, 选取适当的基函数使得系数矩阵稀疏, 对非线性方程中的非线性项采用在 Chebyshev-Gauss- Lobatto 点上的插值进行计算. 最后通过一些数值算例验证了算法的有效性. In this paper, we propose the multi-domain space-time spectral method in time for the fifth-order partial differential equation. Legendre-Petrov-Galerkin method is applied in space direction, and multi-domain Legendre-tau method is applied in time direction, that is: dividing the time interval into multiple domains and Legendre-tau method is applied in each domain. At the same time, the error analysis of the method on linear problems is given in this paper, and we choose proper basis functions to make the coefficient matrix sparse, the nonlinear term for the nonlinear equation is computed by interpolation through Chebyshev-Gauss-Lobatto points. Finally, some numerical examples are given to verify the effectiveness of the algorithm.
君康 慧
Published: 1 January 2021
Pure Mathematics, Volume 11, pp 1067-1075; https://doi.org/10.12677/pm.2021.116121

Abstract:
运用锥上的 Krasnoselskii’s 不动点定理,考虑了二阶积分边值问题 多个正解的存在性,其中0 2是参数,f:[0,1]×[0,∞)→[0,∞)是连续函数,a:[0,1]→[0,+∞)是连续函数,且在[0,1]的任一子区间上不恒为零. In this paper, we study existence of multiple positive solutions for second-order ordinary differential equations with integral boundary problem by the Krasnoselskii’s fixed point theorem on cones. where 0 2 is a parameter, f:[0,1]×[0,∞)→[0,∞) is continuous, a:[0,1]→[0,+∞) is continuous, and a(t) ≢ 0 on any subinterval of [0,1].
林 薇
Published: 1 January 2021
Pure Mathematics, Volume 11, pp 1076-1083; https://doi.org/10.12677/pm.2021.116122

Abstract:
本文运用了值分布理论,证明了亚纯函数与其导数分担两个有穷的公共值和一定的限制条件下,它们必恒等。 In this paper, the value distribution theory is used to prove that meromorphic functions and their derivatives share two finite common values and certain limiting conditions, and they must be identical.
玉苏普阿迪莱•
Published: 1 January 2021
Pure Mathematics, Volume 11, pp 1130-1136; https://doi.org/10.12677/pm.2021.116127

Abstract:
本文通过选取合适的辅助函数,考虑三种情况并利用极值原理来证平均曲率型方程的全局梯度估计。 In this paper, by selecting the appropriate auxiliary function, three cases are considered and the extremum principle is used to prove the global gradient estimation of the mean curvature type equation.
丽赵 亚
Published: 1 January 2021
Pure Mathematics, Volume 11, pp 1121-1129; https://doi.org/10.12677/pm.2021.116126

Abstract:
运用 Krasnoselskii 不动点定理, 本文考虑 p-Laplacian 混合边值问题 负的径向凸解的存在性, 其中B1 = {x ∈ ℝN: |x| p(s) = |s|p−2s, p > 1,f : [0,1] × [0,∞) → [0,∞) 连续. In this paper, by using Krasnoselskii fixed point throrem, we consider the existence of negative radial convex solutions for mixed boundary value problem of p-Laplacian where B1 = {x ∈ ℝN: |x| p(s) = |s|p−2s, p > 1,f : [0,1] × [0,∞) → [0,∞) is continuous.
波丁 利
Published: 1 January 2021
Pure Mathematics, Volume 11, pp 1156-1165; https://doi.org/10.12677/pm.2021.116130

Abstract:
本文主要研究了无限滞后测度泛函微分方程的Φ有界变差解的存在性,借助Kurzweil积分和Φ有界变差函数理论,建立了无限滞后测度泛函微分方程的Φ有界变差解的存在性定理,这是对无限滞后测度泛函微分方程和Kurzweil积分相关结果的推广。 In this paper, we mainly research the existence theorem of bounded Φ-variation solution for measure functional differential equations with infinite delay. The existence theorem of bounded Φ-variation solution to measure functional differential equations with infinite delay is established by using Kurzweil integral and the function of bounded Φ-variation. The result is a generalization of the existence theorem of the measure functional differential equations with infinite delay and Kurzweil integral.
芳张 传
Published: 1 January 2021
Pure Mathematics, Volume 11, pp 1202-1210; https://doi.org/10.12677/pm.2021.116133

Abstract:
对正项级数的达朗贝尔判别法进行了推广,并通过实例说明了推广的判别方法的有效性和实用性。 This paper gives some generalized results on the basis of value of ratio criterion. Finally, some examples are given to demonstrate the effectiveness and practicability of the generalized method.
娟吕 文
Published: 1 January 2021
Pure Mathematics, Volume 11, pp 1250-1256; https://doi.org/10.12677/pm.2021.116138

Abstract:
本文研究具有避难所的平方根功能反应捕食者–食饵模型的Hopf分支的方向和分支周期解的稳定性。结果表明,当避难所作为参数等于一个阈值时,它会发生Hopf分支。 In this paper, we investigate the direction of Hopf bifurcation and the stability of periodic solution of the bifurcation in a predator-prey model with the square root functional response. The results show that Hopf bifurcation occurs when the refuge as a parameter is equal to a threshold.
丹孙 李
Published: 1 January 2021
Pure Mathematics, Volume 11, pp 1230-1241; https://doi.org/10.12677/pm.2021.116136

Abstract:
本文研究了无血管期肿瘤生长的相场模型。该模型耦合了营养物质浓度n的Allen-Cahn方程和序参数 的Cahn-Hilliard方程,描述了肿瘤生长所需营养物质的扩散过程和肿瘤的演变过程。在本文中,我证明了初边值问题弱解的存在性,一维情况下解的唯一性以及稳态解的存在性。 In this paper, we study the solutions to an initial-boundary value problem for a phase-field model of tumor growth, which is the Allen-Cahn equation for the nutrient concentration n coupled with the Cahn-Hilliard equation for the order parameter , and describes the diffusion process of nutrient and the evolution process of tumor. I prove the existence of weak solutions to the problem and the uniqueness of global solution in one dimension. Finally, the existence of stationary solutions is proved.
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