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Electronic Journal of Differential Equations最新文献

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Optimal mass of structure with motion described by Sturm-Liouville operator: design and predesign 由 Sturm-Liouville 算子描述运动的结构的最佳质量：设计和预先设计
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2024-01-24 DOI: 10.58997/ejde.2024.08
B. Belinskiy, Tanner A. Smith
{"title":"Optimal mass of structure with motion described by Sturm-Liouville operator: design and predesign","authors":"B. Belinskiy, Tanner A. Smith","doi":"10.58997/ejde.2024.08","DOIUrl":"https://doi.org/10.58997/ejde.2024.08","url":null,"abstract":"We find an optimal design of a structure described by a Sturm-Liouville (S-L) problem with a spectral parameter in the boundary conditions. Using an approach from calculus of variations, we determine a set of critical points of a corresponding mass functional. However, these critical points - which we call predesigns - do not necessarily themselves represent meaningful solutions: it is of course natural to expect a mass to be real and positive. This represents a generalization of previous work on the topic in several ways. First, previous work considered only boundary conditions and S-L coefficients under certain simplifying assumptions. Principally, we do not assume that one of the coefficients vanishes as in the previous work. Finally, we introduce a set of solvability conditions on the S-L problem data, confirming that the corresponding critical points represent meaningful solutions we refer to as designs. Additionally, we present a natural schematic for testing these conditions, as well as suggesting a code and several numerical examples. \u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/08/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139600555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence and stabilization for impulsive differential equations of second order with multiple delays 具有多重延迟的二阶脉冲微分方程的存在性和稳定性
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2024-01-23 DOI: 10.58997/ejde.2024.07
Sandra Pinelas, O. Tunç, Erdal Korkmaz, C. Tunç
{"title":"Existence and stabilization for impulsive differential equations of second order with multiple delays","authors":"Sandra Pinelas, O. Tunç, Erdal Korkmaz, C. Tunç","doi":"10.58997/ejde.2024.07","DOIUrl":"https://doi.org/10.58997/ejde.2024.07","url":null,"abstract":"Existence and stability of solutions are important parts in the qualitative study of delay differential equations. The stabilizing by imposing proper impulse controls are used in many areas of natural sciences and engineering. This article provides sufficient conditions for the existence and exponential stabilization of solutions to delay impulsive differential equations of second-order with multiple delays. The main tools in this article are the Schaefer fixed point theorem, fixed impulse effects, and Lyapunov-Krasovskii functionals. The outcomes extend earlier results in the literature.\u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/07/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139602948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence of two infinite families of solutions for singular superlinear equations on exterior domains 外部域上奇异超线性方程两个无穷解族的存在性
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2024-01-23 DOI: 10.58997/ejde.2024.06
J. Iaia
{"title":"Existence of two infinite families of solutions for singular superlinear equations on exterior domains","authors":"J. Iaia","doi":"10.58997/ejde.2024.06","DOIUrl":"https://doi.org/10.58997/ejde.2024.06","url":null,"abstract":"In this article we study radial solutions of (Delta u + K(|x|) f(u) =0) inthe exterior of the ball of radius (R>0) in (mathbb {R}^{N}) with (N>2) where (f) grows superlinearly at infinity and is singular at (0) with (f(u) sim frac{1}{|u|^{q-1}u}) and (0<q<1) for small (u).We assume (K(|x|) sim |x|^{-alpha}) for large (|x|) and establish existence of two infinite families of sign-changing solutions when (N+q(N-2) <alpha <2(N-1)).\u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/06/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139603000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global well-posedness for Cauchy problems of Zakharov-Kuznetsov equations on cylindrical spaces 圆柱空间上扎哈罗夫-库兹涅佐夫方程的考奇问题的全局好求解性
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2024-01-22 DOI: 10.58997/ejde.2024.05
Satoshi Osawa, Hideo Takaoka
{"title":"Global well-posedness for Cauchy problems of Zakharov-Kuznetsov equations on cylindrical spaces","authors":"Satoshi Osawa, Hideo Takaoka","doi":"10.58997/ejde.2024.05","DOIUrl":"https://doi.org/10.58997/ejde.2024.05","url":null,"abstract":"We study the global well-posedness of the Zakharov-Kuznetsov equation on cylindrical spaces. Our goal is to establish the existence of global-in-time solutions below the energy class. To prove the results, we adapt the I-method to extend the local solutions globally in time. The main tool in our argument is multilinear estimates in the content of Bourgain's spaces. Using modified energies induced \u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/05/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139609064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global existence and asymptotic profile for a damped wave equation with variable-coefficient diffusion 具有可变系数扩散的阻尼波方程的全局存在性和渐近曲线
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2024-01-08 DOI: 10.58997/ejde.2024.04
Yuequn Li, Hui Liu, Fei Guo
{"title":"Global existence and asymptotic profile for a damped wave equation with variable-coefficient diffusion","authors":"Yuequn Li, Hui Liu, Fei Guo","doi":"10.58997/ejde.2024.04","DOIUrl":"https://doi.org/10.58997/ejde.2024.04","url":null,"abstract":"We considered a Cauchy problem of a one-dimensional semilinear wave equation with variable-coefficient diffusion, time-dependent damping, and perturbations. The global well-posedness and the asymptotic profile are given by employing scaling variables and the energy method. The lower bound estimate of the lifespan to the solution is obtained as a byproduct. \u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/04/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139445558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Strange non-local operators homogenizing the Poisson equation with dynamical unilateral boundary conditions: asymmetric particles of critical size 具有动态单边边界条件的同质化泊松方程的奇异非局部算子：临界大小的非对称粒子
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2024-01-04 DOI: 10.58997/ejde.2024.03
Jesus Ildefonso Diaz, T. Shaposhnikova, Alexander V. Podolskiy
{"title":"Strange non-local operators homogenizing the Poisson equation with dynamical unilateral boundary conditions: asymmetric particles of critical size","authors":"Jesus Ildefonso Diaz, T. Shaposhnikova, Alexander V. Podolskiy","doi":"10.58997/ejde.2024.03","DOIUrl":"https://doi.org/10.58997/ejde.2024.03","url":null,"abstract":"We study the homogenization of a nonlinear problem given by the Poisson equation, in a domain with arbitrarily shaped perforations (or particles) and with a dynamic unilateral boundary condition (of Signorini type), with a large coefficient, on the boundary of these perforations (or particles). This problem arises in the study of chemical reactions of zero order. The consideration of a possible asymmetry in the perforations (or particles) is fundamental for considering some applications in nanotechnology, where symmetry conditions are too restrictive. It is important also to consider perforations (or particles) constituted by small different parts and then with several connected components. We are specially concerned with the so-called critical case in which the relation between the coefficient in the boundary condition, the period of the basic structure, and the size of the holes (or particles) leads to the appearance of an unexpected new term in the effective homogenized equation. Because of the dynamic nature of the boundary condition this ``strange term'' becomes now a non-local in time and non-linear operator. We prove a convergence theorem and find several properties of the ``strange operator'' showing that there is a kind of regularization through the homogenization process. \u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/03/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139387168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability and rate of decay for solutions to stochastic differential equations with Markov switching 带有马尔可夫开关的随机微分方程解的稳定性和衰减率
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2024-01-03 DOI: 10.58997/ejde.2024.01
Shuaishuai Lu, Xue Yang
{"title":"Stability and rate of decay for solutions to stochastic differential equations with Markov switching","authors":"Shuaishuai Lu, Xue Yang","doi":"10.58997/ejde.2024.01","DOIUrl":"https://doi.org/10.58997/ejde.2024.01","url":null,"abstract":"In this article, we present the almost sure asymptotic stability and a general rate of decay for solutions to stochastic differential equations (SDEs) with Markov switching. By establishing a suitable Lyapunov function and using an exponential Martingale inequality and the Borel-Cantelli theorem, we give sufficient conditions for the asymptotic stability. Also, we obtain sufficient conditions for the construction of two kinds of Lyapunov functions. Finally give two examples to illustrate the validity of our results.\u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/01/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139387708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
KAM theorem for degenerate infinite-dimensional reversible systems 退化无限维可逆系统的 KAM 定理
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2024-01-03 DOI: 10.58997/ejde.2024.02
Zhaowei Lou, Youchao Wu
{"title":"KAM theorem for degenerate infinite-dimensional reversible systems","authors":"Zhaowei Lou, Youchao Wu","doi":"10.58997/ejde.2024.02","DOIUrl":"https://doi.org/10.58997/ejde.2024.02","url":null,"abstract":"In this article, we establish a Kolmogorov-Arnold-Moser (KAM) theorem for degenerate infinite-dimensional reversible systems under a non-degenerate condition of Russmann type. This theorem broadens the scope of applicability of degenerate KAM theory, previously confined to Hamiltonian systems, by incorporating infinite-dimensional reversible systems. Using this theorem, we obtain the existence and linear stability of quasi-periodic solutions for a class of non-Hamiltonian but reversible beam equations with non-linearities in derivatives.\u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/02/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139389609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic stabilization for Bresse transmission systems with fractional damping 具有分数阻尼的布雷斯传动系统的渐近稳定问题
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-12-28 DOI: 10.58997/ejde.2023.87
Jianghao Hao, Dingkun Wang
{"title":"Asymptotic stabilization for Bresse transmission systems with fractional damping","authors":"Jianghao Hao, Dingkun Wang","doi":"10.58997/ejde.2023.87","DOIUrl":"https://doi.org/10.58997/ejde.2023.87","url":null,"abstract":"In this article, we study the asymptotic stability of Bresse transmission systems with two fractional dampings. The dissipation mechanism of control is given by the fractional damping term and acts on two equations. The relationship between the stability of the system, the fractional damping index (thetain[0,1]) and the different wave velocities is obtained. By using the semigroup method, we obtain the well-posedness of the system. We also prove that when the wave velocities are unequal or equal with (thetaneq 0), the system is not exponential stable, and it is polynomial stable. In addition, the precise decay rate is obtained by the multiplier method and the frequency domain method. When the wave velocities are equal with (theta=0), the system is exponential stable. For more information see https://ejde.math.txstate.edu/Volumes/2023/87/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139151298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global low-energy weak solutions for compressible magneto-micropolar fluids with discontinuous initial data in R^3 R^3 中初始数据不连续的可压缩磁微波流体的全局低能弱解
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-12-20 DOI: 10.58997/ejde.2023.86
Wanping Wu, Yinghui Zhang
{"title":"Global low-energy weak solutions for compressible magneto-micropolar fluids with discontinuous initial data in R^3","authors":"Wanping Wu, Yinghui Zhang","doi":"10.58997/ejde.2023.86","DOIUrl":"https://doi.org/10.58997/ejde.2023.86","url":null,"abstract":"This article concerns the weak solutions of a 3D Cauchy problem of compressible magneto-micropolar fluids with discontinuous initial data. Under the assumption that the initial data are of small energy and the initial density is positive and essentially bounded, we establish the existence of weak solutions that are global-in-time. Moreover, we obtain the large-time behavior of such solutions. \u0000For moreinformation see https://ejde.math.txstate.edu/Volumes/2023/86/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138956127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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