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Bifurcation analysis of a single species reaction-diffusion model with nonlocal delay 一类非局部时滞单组分反应扩散模型的分岔分析
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2020-01-01 DOI: 10.4134/JKMS.J190036
Jun Zhou
{"title":"Bifurcation analysis of a single species reaction-diffusion model with nonlocal delay","authors":"Jun Zhou","doi":"10.4134/JKMS.J190036","DOIUrl":"https://doi.org/10.4134/JKMS.J190036","url":null,"abstract":"A reaction-diffusion model with spatiotemporal delay modeling the dynamical behavior of a single species is investigated. The parameter regions for the local stability, global stability and instability of the unique positive constant steady state solution are derived. The conditions of the occurrence of Turing (diffusion-driven) instability are obtained. The existence of time-periodic solutions, the existence and nonexistence of nonconstant positive steady state solutions are proved by bifurcation method and energy method. Numerical simulations are presented to verify and illustrate the theoretical results.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70511282","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
WEIGHTED HARDY INEQUALITIES WITH SHARP CONSTANTS 具有尖锐常数的加权hardy不等式
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2020-01-01 DOI: 10.4134/JKMS.J190266
A. Kalybay, R. Oinarov
{"title":"WEIGHTED HARDY INEQUALITIES WITH SHARP CONSTANTS","authors":"A. Kalybay, R. Oinarov","doi":"10.4134/JKMS.J190266","DOIUrl":"https://doi.org/10.4134/JKMS.J190266","url":null,"abstract":"In the paper, we establish the validity of the weighted discrete and integral Hardy inequalities with periodic weights and find the best possible constants in these inequalities. In addition, by applying the established discrete Hardy inequality to a certain second–order difference equation, we discuss some oscillation and nonoscillation results.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70511200","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: 3
GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR IN A THREE-DIMENSIONAL TWO-SPECIES CHEMOTAXIS-STOKES SYSTEM WITH TENSOR-VALUED SENSITIVITY 具有张量值灵敏度的三维两物种趋化- stokes系统的全局存在性和渐近行为
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2020-01-01 DOI: 10.4134/JKMS.J190028
B. Liu, Guoqiang Ren
{"title":"GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR IN A THREE-DIMENSIONAL TWO-SPECIES CHEMOTAXIS-STOKES SYSTEM WITH TENSOR-VALUED SENSITIVITY","authors":"B. Liu, Guoqiang Ren","doi":"10.4134/JKMS.J190028","DOIUrl":"https://doi.org/10.4134/JKMS.J190028","url":null,"abstract":". In this paper, we deal with a two-species chemotaxis-Stokes system with Lotka-Volterra competitive kinetics under homogeneous Neu- mann boundary conditions in a general three-dimensional bounded domain with smooth boundary. Under appropriate regularity assumptions on the initial data, by some L p -estimate techniques, we show that the system possesses at least one global and bounded weak solution, in addi- tion to discussing the asymptotic behavior of the solutions. Our results generalizes and improves partial previously known ones.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70511233","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: 15
ON A FAMILY OF COHOMOLOGICAL DEGREES 在上同调度的族上
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2020-01-01 DOI: 10.4134/JKMS.J190305
D. T. Cuong, Pham Hong Nam
{"title":"ON A FAMILY OF COHOMOLOGICAL DEGREES","authors":"D. T. Cuong, Pham Hong Nam","doi":"10.4134/JKMS.J190305","DOIUrl":"https://doi.org/10.4134/JKMS.J190305","url":null,"abstract":"Cohomological degrees (or extended degrees) were introduced by Doering, Gunston and Vasconcelos as measures for the complexity of structure of finitely generated modules over a Noetherian ring. Until now only very few examples of such functions have been known. Using a Cohen-Macaulay obstruction defined earlier, we construct an infinite family of cohomological degrees.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70511274","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
WEIGHTED MOORE-PENROSE INVERSES OF ADJOINTABLE OPERATORS ON INDEFINITE INNER-PRODUCT SPACES 不定内积空间上可伴算子的加权摩尔-彭罗斯逆
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2020-01-01 DOI: 10.4134/JKMS.J190306
Mengjie Qin, Qingxiang Xu, Ali Zamani
{"title":"WEIGHTED MOORE-PENROSE INVERSES OF ADJOINTABLE OPERATORS ON INDEFINITE INNER-PRODUCT SPACES","authors":"Mengjie Qin, Qingxiang Xu, Ali Zamani","doi":"10.4134/JKMS.J190306","DOIUrl":"https://doi.org/10.4134/JKMS.J190306","url":null,"abstract":". Necessary and sufficient conditions are provided under which the weighted Moore–Penrose inverse A † MN exists, where A is an ad- jointable operator between Hilbert C ∗ -modules, and the weights M and N are only self-adjoint and invertible. Relationship between weighted Moore–Penrose inverses A † MN is clarified when A is fixed, whereas M and N are variable. Perturbation analysis for the weighted Moore–Penrose inverse is also provided.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70511315","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: 3
FRACTIONAL ORDER SOBOLEV SPACES FOR THE NEUMANN LAPLACIAN AND THE VECTOR LAPLACIAN 分数阶sobolev空间的诺伊曼拉普拉斯算子和向量拉普拉斯算子
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2020-01-01 DOI: 10.4134/JKMS.J190351
Seungil Kim
{"title":"FRACTIONAL ORDER SOBOLEV SPACES FOR THE NEUMANN LAPLACIAN AND THE VECTOR LAPLACIAN","authors":"Seungil Kim","doi":"10.4134/JKMS.J190351","DOIUrl":"https://doi.org/10.4134/JKMS.J190351","url":null,"abstract":". In this paper we study fractional Sobolev spaces characterized by a norm based on eigenfunction expansions. The goal of this paper is twofold. The first one is to define fractional Sobolev spaces of order − 1 ≤ s ≤ 2 equipped with a norm defined in terms of Neumann eigen- function expansions. Due to the zero Neumann trace of Neumann eigenfunctions on a boundary, fractional Sobolev spaces of order 3 / 2 ≤ s ≤ 2 characterized by the norm are the spaces of functions with zero Neumann trace on a boundary. The spaces equipped with the norm are useful for studying cross-sectional traces of solutions to the Helmholtz equation in waveguides with a homogeneous Neumann boundary condition. The sec- ond one is to define fractional Sobolev spaces of order − 1 ≤ s ≤ 1 for vector-valued functions in a simply-connected, bounded and smooth do- main in R 2 . These spaces are defined by a norm based on series expansions in terms of eigenfunctions of the vector Laplacian with boundary condi- tions of zero tangential component or zero normal component. The spaces defined by the norm are important for analyzing cross-sectional traces of time-harmonic electromagnetic fields in perfectly conducting waveguides.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70511511","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: 6
AN EVALUATION FORMULA FOR A GENERALIZED CONDITIONAL EXPECTATION WITH TRANSLATION THEOREMS OVER PATHS 具有路径平移定理的广义条件期望的求值公式
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2020-01-01 DOI: 10.4134/JKMS.J190133
D. Cho
{"title":"AN EVALUATION FORMULA FOR A GENERALIZED CONDITIONAL EXPECTATION WITH TRANSLATION THEOREMS OVER PATHS","authors":"D. Cho","doi":"10.4134/JKMS.J190133","DOIUrl":"https://doi.org/10.4134/JKMS.J190133","url":null,"abstract":". Let C [0 ,T ] denote an analogue of Wiener space, the space of real-valued continuous functions on the interval [0 ,T ]. For a partition 0 = t 0 < t 1 < ··· < t n < t n +1 = T of [0 ,T ], define X n : C [0 ,T ] → R n +1 by X n ( x ) = ( x ( t 0 ) ,x ( t 1 ) ,...,x ( t n )). In this paper we derive a simple evaluation formula for Radon-Nikodym derivatives similar to the conditional expectations of functions on C [0 ,T ] with the conditioning function X n which has a drift and does not contain the present position of paths. As applications of the formula with X n , we evaluate the Radon-Nikodym derivatives of the functions (cid:82) T 0 [ x ( t )] m dλ ( t )( m ∈ N ) and [ (cid:82) T 0 x ( t ) dλ ( t )] 2 on C [0 ,T ], where λ is a complex-valued Borel measure on [0 ,T ]. Finally we derive two translation theorems for the Radon-Nikodym derivatives of the functions on C [0 ,T ].","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70511527","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: 3
REGULARITY AND MULTIPLICITY OF SOLUTIONS FOR A NONLOCAL PROBLEM WITH CRITICAL SOBOLEV-HARDY NONLINEARITIES 一类临界sobolev-hardy非线性非局部问题解的正则性和多重性
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2020-01-01 DOI: 10.4134/JKMS.J190367
S. Alotaibi, K. Saoudi
{"title":"REGULARITY AND MULTIPLICITY OF SOLUTIONS FOR A NONLOCAL PROBLEM WITH CRITICAL SOBOLEV-HARDY NONLINEARITIES","authors":"S. Alotaibi, K. Saoudi","doi":"10.4134/JKMS.J190367","DOIUrl":"https://doi.org/10.4134/JKMS.J190367","url":null,"abstract":"In this work we investigate the nonlocal elliptic equation with critical Hardy-Sobolev exponents as follows, (P) (−∆p)su = λ|u|q−2u+ |u| ps (t)−2u |x|t in Ω, u = 0 in RN Ω, where Ω ⊂ RN is an open bounded domain with Lipschitz boundary, 0 < s < 1, λ > 0 is a parameter, 0 < t < sp < N , 1 < q < p < ps where ps = Np N−sp , p ∗ s(t) = p(N−t) N−sp , are the fractional critical Sobolev and Hardy-Sobolev exponents respectively. The fractional p-laplacian (−∆p)u with s ∈ (0, 1) is the nonlinear nonlocal operator defined on smooth functions by (−∆p)u(x) = 2 lim ↘0 ∫ RNB |u(x)− u(y)|p−2(u(x)− u(y)) |x− y|N+ps dy, x ∈ R . The main goal of this work is to show how the usual variational methods and some analysis techniques can be extended to deal with nonlocal problems involving Sobolev and Hardy nonlinearities. We also prove that for some α ∈ (0, 1), the weak solution to the problem (P) is in C1,α(Ω).","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70511626","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
BIFURCATION PROBLEM FOR A CLASS OF QUASILINEAR FRACTIONAL SCHRÖDINGER EQUATIONS 一类拟线性分数阶schrÖdinger方程的分岔问题
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2020-01-01 DOI: 10.4134/JKMS.J190646
I. Abid
{"title":"BIFURCATION PROBLEM FOR A CLASS OF QUASILINEAR FRACTIONAL SCHRÖDINGER EQUATIONS","authors":"I. Abid","doi":"10.4134/JKMS.J190646","DOIUrl":"https://doi.org/10.4134/JKMS.J190646","url":null,"abstract":"We study bifurcation for the following fractional Schrödinger equation  (−∆)su+ V (x)u = λ f(u) in Ω u > 0 in Ω u = 0 inRn Ω where 0 < s < 1, n > 2s, Ω is a bounded smooth domain of Rn, (−∆)s is the fractional Laplacian of order s, V is the potential energy satisfying suitable assumptions and λ is a positive real parameter. The nonlinear term f is a positive nondecreasing convex function, asymptotically linear that is lim t→+∞ f(t) t = a ∈ (0,+∞). We discuss the existence, uniqueness and stability of a positive solution and we also prove the existence of critical value and the uniqueness of extremal solutions. We take into account the types of Bifurcation problem for a class of quasilinear fractional Schrödinger equations, we also establish the asymptotic behavior of the solution around the bifurcation point.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70512396","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
Lower order eigenvalues for the bi-drifting Laplacian on the Gaussian shrinking soliton 高斯收缩孤子上双漂移拉普拉斯算子的低阶特征值
IF 0.6 4区 数学
Journal of the Korean Mathematical Society Pub Date : 2020-01-01 DOI: 10.4134/JKMS.J190737
Lingzhong Zeng
{"title":"Lower order eigenvalues for the bi-drifting Laplacian on the Gaussian shrinking soliton","authors":"Lingzhong Zeng","doi":"10.4134/JKMS.J190737","DOIUrl":"https://doi.org/10.4134/JKMS.J190737","url":null,"abstract":"It may very well be difficult to prove an eigenvalue inequality of Payne-Pólya-Weinberger type for the bi-drifting Laplacian on the bounded domain of the general complete metric measure spaces. Even though we suppose that the differential operator is bi-harmonic on the standard Euclidean sphere, this problem still remains open. However, under certain condition, a general inequality for the eigenvalues of bidrifting Laplacian is established in this paper, which enables us to prove an eigenvalue inequality of Ashbaugh-Cheng-Ichikawa-Mametsuka type (which is also called an eigenvalue inequality of Payne-Pólya-Weinberger type) for the eigenvalues with lower order of bi-drifting Laplacian on the Gaussian shrinking soliton.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70513335","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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