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SUFFICIENT AND NECESSARY CONDITIONS ON THE EXISTENCE AND ESTIMATES OF BOUNDARY BLOW-UP SOLUTIONS FOR SINGULAR p-LAPLACIAN EQUATIONS
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作者 张学梅 阚士坤 《Acta Mathematica Scientia》 SCIE CSCD 2023年第3期1175-1194,共20页
Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we pro... Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p-Laplacian problem△_(p)u=b(x)g(u)for x∈Ω,u(x)→+∞as dist(x,■Ω)→0.The estimates of such solutions are also investigated.Moreover,when b has strong singularity,the nonexistence of boundary blow-up(radial)solutions and infinitely many radial solutions are also considered. 展开更多
关键词 singular p-Laplacian equation boundary blow-up sub-supersolution method EXISTENCE nonexistence and estimates sufficient and necessary conditions
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ON THE NECESSARY AND SUFFICIENT CONDITIONS TO SOLVE A HEAT EQUATION WITH GENERAL ADDITIVE GAUSSIAN NOISE 被引量:2
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作者 Yaozhong HU Yanghui LIU 《Acta Mathematica Scientia》 SCIE CSCD 2019年第3期669-690,共22页
In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equ... In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two differen t met hods, respectively, based on variance compu tations and on pat h-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution. 展开更多
关键词 Stochastic heat equation general Gaussian noise L^(2) solution sufficient and necessary condition Wong-Zakai approximation pathwise solution Holder continuity Besov space
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THE SUFFICIENT AND NECESSARY CONDITION OF THE MAJOR STOCHASTIC PREFERENCE RULE IN GROUP DECISION MAKING 被引量:1
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作者 Fan YE Naiming DONG +1 位作者 Jing LI Zhenjie HONG 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2012年第5期942-949,共8页
Group decision making problem with stochastic preference is investigated. The authors present four rational conditions for testing group stochastic preference rule, and prove that the com- bination of these four ratio... Group decision making problem with stochastic preference is investigated. The authors present four rational conditions for testing group stochastic preference rule, and prove that the com- bination of these four rational conditions is the sufficient and necessary condition of major stochastic preference rule for group stochastic preference rule. 展开更多
关键词 Group decision making group stochastic preference rule major stochastic preferencerule stochastic preference sufficient and necessary condition.
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Some Necessary and Sufficient Condition of Multivariate Random Variable Satisfy Normal Distribution
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作者 伍俊良 秦志仁 《Chinese Quarterly Journal of Mathematics》 CSCD 1996年第1期39-41,共3页
In this paper,we extended some results of article[1],obtain some sufficient and necessary condition which multivariate random variable satisfy normal distribution.
关键词 multivariate random variable normal distribution:sufficient and necessary condition
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Solution of the Matrix Second Semi-Tensor Product Equation A ∘ l X ∘ l B=C
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作者 Hao Zhang 《Journal of Applied Mathematics and Physics》 2024年第10期3261-3280,共20页
In this paper, the solution of the matrix second semi-tensor product equation A∘lX∘lB=Cis studied. Firstly, the solvability of the matrix-vector second semi-tensor product equation is investigated. At the same time,... In this paper, the solution of the matrix second semi-tensor product equation A∘lX∘lB=Cis studied. Firstly, the solvability of the matrix-vector second semi-tensor product equation is investigated. At the same time, the compatibility conditions, the sufficient and necessary conditions and the specific solution methods for the matrix solution are given. Secondly, we further consider the solvability of the second semi-tensor product equation of the matrix. For each part, several examples are given to illustrate the validity of the results. 展开更多
关键词 Matrix Equation The Second Semi-Tensor Product Compatibility condition sufficient and necessary conditions VECTORIZATION
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Network Decomposition and Maximum Independent Set Part Ⅰ:Theoretic Basis
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作者 朱松年 朱嫱 《Journal of Southwest Jiaotong University(English Edition)》 2003年第2期103-121,共19页
The structure and characteristics of a connected network are analyzed, and a special kind of sub-network, which can optimize the iteration processes, is discovered. Then, the sufficient and necessary conditions for o... The structure and characteristics of a connected network are analyzed, and a special kind of sub-network, which can optimize the iteration processes, is discovered. Then, the sufficient and necessary conditions for obtaining the maximum independent set are deduced. It is found that the neighborhood of this sub-network possesses the similar characters, but both can never be allowed incorporated together. Particularly, it is identified that the network can be divided into two parts by a certain style, and then both of them can be transformed into a pair sets network, where the special sub-networks and their neighborhoods appear alternately distributed throughout the entire pair sets network. By use of this characteristic, the network decomposed enough without losing any solutions is obtained. All of these above will be able to make well ready for developing a much better algorithm with polynomial time bound for an odd network in the the application research part of this subject. 展开更多
关键词 odd network network transformation and decomposition negative envelope graph and pseudo-negative envelope graph the sufficient and necessary conditions polynomial time.
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ON THE BELTRAMI FLOWS 被引量:3
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作者 是长春 黄永念 陈耀松 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 1992年第4期289-294,共6页
To illustrate the general properties of the Beltrami flows,a new sufficient and necessary condi- tion of the general solution of the Beltrami flows has been given,on whose basis some sufficient and necessary condition... To illustrate the general properties of the Beltrami flows,a new sufficient and necessary condi- tion of the general solution of the Beltrami flows has been given,on whose basis some sufficient and necessary conditions and sufficient conditions in literature are unified.The advantages of the new expressions are that one may get solutions of Beltrami flows with constant proportional factors which satisfy some given asymptotic decaying conditions at infinity.Finally,we find a class of spherical vortices of Beltrami flows,where the mo- tion trajectories of the fluid particles are confined within a sphere or two adjacent concentric spherical shells.We find that the superpositions of the spherical vortices of the same order with different polar axes may produce chaotic trajectories. 展开更多
关键词 Beltrami flow sufficient and necessary condition spherica vortex chaotic trajectory
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On the Construction and Analysis of Finite Volume Element Schemes with Optimal L^(2) Convergence Rate
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作者 Xiang Wang Yuqing Zhang 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE CSCD 2021年第1期47-70,共24页
We provide a general construction method for a finite volume element(FVE)scheme with the optimal L^(2)convergence rate.The k-(k-1)-order orthogonal condition(generalized)is proved to be a sufficient and necessary cond... We provide a general construction method for a finite volume element(FVE)scheme with the optimal L^(2)convergence rate.The k-(k-1)-order orthogonal condition(generalized)is proved to be a sufficient and necessary condition for a k-order FVE scheme to have the optimal L^(2) convergence rate in 1D,in which the independent dual parameters constitute a(k-1)-dimension surface in the reasonable domain in k-dimension.In the analysis,the dual strategies in different primary elements are not necessarily to be the same,and they are allowed to be asymmetric in each primary element,which open up more possibilities of the FVE schemes to be applied to some complex problems,such as the convection-dominated problems.It worth mentioning that,the construction can be extended to the quadrilateral meshes in 2D.The stability and H^(1) estimate are proved for completeness.All the above results are demon-strated by numerical experiments. 展开更多
关键词 Finite volume L^(2)estimate sufficient and necessary condition orthogonal condition
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Optimal vaccination strategy for a mean-field stochastic susceptible-infected-vaccinated system
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作者 Zong Wang Qimin Zhang 《International Journal of Biomathematics》 SCIE 2023年第1期1-27,共27页
The parameters of biological system may change under the influence of different states or state processes.The change of parameters can also affect the dynamic behaviors of epidemic disease.This paper presents a mean f... The parameters of biological system may change under the influence of different states or state processes.The change of parameters can also affect the dynamic behaviors of epidemic disease.This paper presents a mean field stochastic susceptible-infectedvaccinated(SIV)epidemic model which parameters depend on the state process.The sufficient and necessary conditions of optimal control of the novel epidemic model are obtained by maximum principle.Finally,we perform representative numerical simulations to illustrate the theoretical results and further discuss the feasibility based on the hand,foot and mouth disease(HFMD)data in China. 展开更多
关键词 Mean-field stochastic differential equation stochastic maximum principle SIV epidemic model variational inequality sufficient and necessary conditions.
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MODIFIED LEAST SQUARE METHOD ON COMPUTING DIRICHLET PROBLEMS 被引量:1
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作者 Sheng Pingxing Tang Zhengquan (Dept. of Math., Shanghai University, Shanghai 200444) 《Annals of Differential Equations》 2006年第3期350-355,共6页
The singularity theory of dynamical systems is linked to the numerical computation of boundary value problems of differential equations. It turns out to be a modified least square method for a calculation of variation... The singularity theory of dynamical systems is linked to the numerical computation of boundary value problems of differential equations. It turns out to be a modified least square method for a calculation of variational problem defined on Ck(Ω), in which the base functions are polynomials and the computation of problems is transferred to compute the coefficients of the base functions. The theoretical treatment and some simple examples are provided for understanding the modification procedure of the methods. A modified least square method on difference scheme is introduced with a general matrix form of dynamical systems. We emphasize the simplicity of the algorithm and only use Euler algorithm to compute initial value problems of ODEs. A better algorithm is needed to reduce the stiffness of ODEs. 展开更多
关键词 equilibria of dynamical systems sufficient and necessary condition on extremes calculus of variation boundary value problems modified least square method
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