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.
{"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":"57 1","pages":"249-281"},"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}
. 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 ].
。设C [0,T]表示区间[0,T]上的实值连续函数空间的一个类似的Wiener空间。对于划分0 = t 0 < t 1 <···< t n < t n +1 = t ([0, t])，定义X n: C [0, t]→R n +1 × X n (X) = (X (t 0)， X (t 1)，…(x (t n))本文导出了一个简单的Radon-Nikodym导数的计算公式，类似于C [0,T]上函数的条件期望，条件函数X n具有漂移且不包含路径的当前位置。作为带X n的公式的应用，我们计算了函数(cid:82) t0 [X (T)] m dλ (T)(m∈n)和[(cid:82) t0 X (T) dλ (T)] 2在C [0,T]上的Radon-Nikodym导数，其中λ是[0,T]上的复值Borel测度。最后导出了C [0,T]上函数的Radon-Nikodym导数的两个平移定理。
{"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":"45 1","pages":"451-470"},"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}
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.
{"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":"57 1","pages":"603-616"},"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}
. 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.
{"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":"57 1","pages":"215-247"},"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}
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.
{"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":"57 1","pages":"669-689"},"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}
. 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.
． 给出了加权Moore-Penrose逆A†MN存在的充分必要条件，其中A是Hilbert C * -模之间的可合算子，且权M和权N仅自伴且可逆。当A固定时，明确了加权Moore-Penrose逆A†MN之间的关系，而M和N是可变的。给出了加权Moore-Penrose逆的摄动分析。
{"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":"57 1","pages":"691-706"},"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}
. 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.
{"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":"57 1","pages":"721-745"},"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}
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).
在这个工作我们调查外地椭圆方程临界Hardy-Sobolev指数如下,(P)(−∆P)苏=λ| u | q−2 u + | | ps (t)−2 u | x | tΩ,在RN u = 0Ω,哪里Ω⊂RN和李普希茨是一个开放的有限域边界,0 < s < 1,λ> 0是一个参数,0 < t < sp < N, 1 < < P < P, P = Np N−sp, P∗s (t) = P (N−t) N−sp,分别是分数重要水列夫和Hardy-Sobolev指数。s∈(0,1)的分数阶p-拉普拉斯算子(−∆p)u是光滑函数上定义的非线性非局部算子，即(−∆p)u(x) = 2 lim ` ` 0∫RNB |u(x)−u(y)|p−2(u(x)−u(y)) |x−y|N+ps dy, x∈R。这项工作的主要目的是展示如何将通常的变分方法和一些分析技术扩展到处理涉及Sobolev和Hardy非线性的非局部问题。我们还证明了对于某些α∈(0,1)，问题(P)的弱解在C1，α(Ω)中。
{"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":"57 1","pages":"747-775"},"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}
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.
我们研究了以下分数阶Schrödinger方程(−∆)su+ V (x)u = λ f(u)在Ω u > 0在Ω u = 0 inRn Ω中的分岔，其中0 < s < 1, n > 2s， Ω是Rn的有界光滑域，(−∆)s是s阶分数阶拉普拉斯算子，V是满足适当假设的势能，λ是一个正实参数。非线性项f是一个正的非降凸函数，其渐近线性为lim t→+∞f(t) t = a∈(0，+∞)。讨论了正解的存在性、唯一性和稳定性，证明了极值解的存在性和唯一性。考虑了一类拟线性分数阶Schrödinger方程的分岔问题的类型，并建立了解在分岔点附近的渐近性态。
{"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":"57 1","pages":"1347-1372"},"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}
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.
{"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":"9 1","pages":"1471-1484"},"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}
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