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一类半线性椭圆型方程正奇异解的存在性
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作者 王世祥 马秋红 《长春大学学报》 2000年第4期16-18,共3页
对Rn 中半线性椭圆型方程利用微分变换和Banach空间紧映射定理给出了其奇异正奇异解的存在性。
关键词 椭圆型方程 半线性 正奇异解 存在性
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一类拟线性椭圆型方程正奇异解的能量估计 被引量:5
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作者 周杰 杨作东 《南京师大学报(自然科学版)》 CAS CSCD 北大核心 2006年第1期21-24,共4页
本文给出了如下问题d iv(|u|p-2 u)+λf(u)=0,x∈Ωu|Ω=0,奇异解的能量估计,其中p≥2,Ω=B1是单位球,λ>0是一个参数.进一步得到了uλ是上述问题的正则正解序列且当λ→λ0∈(0,∞)时逐点收敛于奇异解U,则在Lq+1(B1)和H01(B1)中,当... 本文给出了如下问题d iv(|u|p-2 u)+λf(u)=0,x∈Ωu|Ω=0,奇异解的能量估计,其中p≥2,Ω=B1是单位球,λ>0是一个参数.进一步得到了uλ是上述问题的正则正解序列且当λ→λ0∈(0,∞)时逐点收敛于奇异解U,则在Lq+1(B1)和H01(B1)中,当λ→λ0时uλ收敛于U. 展开更多
关键词 存在性 正奇异解 拟线性椭圆型方程 能量估计
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一类拟线性椭圆型方程正奇异解的存在性 被引量:1
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作者 杨作东 《数学物理学报(A辑)》 CSCD 北大核心 2005年第4期445-450,共6页
该文得到了一类拟线性椭圆型方程在球域(Ω=BR={x∈RN:x<R})或在N维欧氏空间(Ω=B∞=RN,N≥3)上正对称奇异解的存在性定理.其中非线性项f∈C1(R)满足超临界增长性条件.
关键词 存在性 对称奇异 拟线性椭圆型方程
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一个超临界椭圆问题的径向奇异正解(英文)
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作者 赵培浩 张志强 《兰州大学学报(自然科学版)》 CAS CSCD 北大核心 1999年第4期12-16,共5页
对非线性椭圆问题正解的研究具有实际的物理意义,其研究方法主要有拓扑度理论和变分方法.当非线性项是次临界超线性增长时,极小极大定理是最为有力的工具.即使该超线性项是临界增长的,仍可在某能量面以下重建紧性以保证极小极大定... 对非线性椭圆问题正解的研究具有实际的物理意义,其研究方法主要有拓扑度理论和变分方法.当非线性项是次临界超线性增长时,极小极大定理是最为有力的工具.即使该超线性项是临界增长的,仍可在某能量面以下重建紧性以保证极小极大定理是适用的.但是,当该超线性项是超临界增长时,由于没有嵌入定理,Sobolev 空间上的变分方法失效.目前,对超临界问题的研究仅限于讨论其径向对称解,这时该问题转化为常微分方程.注意到球域上该问题的正解均是径向对称的,使用基于压缩映像的不动点定理,通过一系列详细的估计,证明了该问题的具某种奇异性的径向正解的存在惟一性. 展开更多
关键词 超临界椭圆问题 径向奇异 压缩映像 非线性
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一类拟线性椭圆方程奇异正径向解的存在
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作者 赵建清 王万忠 《连云港师范高等专科学校学报》 2005年第2期93-94,共2页
文章主要证明一类二阶椭圆方程奇异正径向解的存在。
关键词 拟线性椭圆方程 奇异径向 存在
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一类奇异拟线性常微分方程两点边值问题解的存在性 被引量:1
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作者 董正华 《河南师范大学学报(自然科学版)》 CAS CSCD 2002年第3期18-20,共3页
本文得到了一类奇异拟线性常微分方程两点边值问题解的存在性和唯一性 .此类问题存在于研究 p- L aplace方程 ,一般反应扩散理论 ,非牛顿流体理论 ,多孔媒质中的气体渗流等问题中 .这一结论是通过使用不动点定理建立的 .
关键词 P-拉普拉斯方程 奇异 存在性 唯一性 奇异拟线性常微分方程 两点边值问题
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一类四阶奇异半正边值问题正解的存在性 被引量:13
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作者 张新光 赵增勤 《系统科学与数学》 CSCD 北大核心 2006年第5期553-560,共8页
利用不动点指数结合平移变换的方法,研究了一类四阶奇异半正边值问题,得到了其C^2[0,1]∩C^4(0,1)正解存在的一个新结果.
关键词 奇异边值问题 超线性
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Banach空间中二阶非线性脉冲奇异微分方程多点无穷边值问题的正解 被引量:3
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作者 李耀红 张晓燕 《系统科学与数学》 CSCD 北大核心 2011年第7期845-858,共14页
利用锥理论和Mnch不动点定理结合单调迭代技巧,研究了Banach空间中一类二阶非线性脉冲奇异微分方程多点无穷边值问题,获得了正解的存在性定理和正解的迭代序列,改进和推广了某些已知结果.
关键词 脉冲奇异微分方程 多点边值问题 MSnch不动点定理.
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带p-Laplacian算子三点奇异边值问题多个对称正解的存在性 被引量:1
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作者 李小平 田元生 葛渭高 《系统科学与数学》 CSCD 北大核心 2012年第11期1419-1426,共8页
利用凸锥上的不动点定理,研究了一类带p-Laplacian算子的微分方程三点奇异边值问题对称正解的多重性,得到了这类边值问题存在多个对称正解的充分条件.
关键词 p-Laplacian算子 三点奇异边值问题 不动点定理 对称
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多重调和Dirichlet问题奇异正解的对称性
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作者 刘忠原 《数学学报(中文版)》 CSCD 北大核心 2022年第1期115-122,共8页
我们在穿孔单位球上研究下面多重调和Dirichlet问题{(-△)^(k)u=f(u),在B\{0}内,u>0,在B\{0}内,u=■u/■v=…=■^(k-1)u/■v^(k-1)=0,在■B上,其中,B是R^(N)中的单位球,v是■B的单位外法向量,N>2k,k≥2.在f满足适当假设条件下,如... 我们在穿孔单位球上研究下面多重调和Dirichlet问题{(-△)^(k)u=f(u),在B\{0}内,u>0,在B\{0}内,u=■u/■v=…=■^(k-1)u/■v^(k-1)=0,在■B上,其中,B是R^(N)中的单位球,v是■B的单位外法向量,N>2k,k≥2.在f满足适当假设条件下,如果0是不可去奇点,我们利用移动平面法得到奇异正解的径向对称性.由此,我们可以得到临界双调和Dirichlet问题正解的不存在性. 展开更多
关键词 奇异的对称性 多重调和问题 移动平面法
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Study on algorithms of low SNR inversion of T_2 spectrum in NMR 被引量:3
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作者 林峰 王祝文 +2 位作者 李静叶 张雪昂 江玉龙 《Applied Geophysics》 SCIE CSCD 2011年第3期233-238,241,共7页
The method of regularization factor selection determines stability and accuracy of the regularization method. A formula of regularization factor was proposed by analyzing the relationship between the improved SVD and ... The method of regularization factor selection determines stability and accuracy of the regularization method. A formula of regularization factor was proposed by analyzing the relationship between the improved SVD and regularization method. The improved SVD algorithm and regularization method could adapt to low SNR. The regularization method is better than the improved SVD in the case that SNR is below 30 and the improved SVD is better than the regularization method when SNR is higher than 30. The regularization method with the regularization factor proposed in this paper can be better applied into low SNR (5〈SNR) NMR logging. The numerical simulations and real NMR data process results indicated that the improved SVD algorithm and regularization method could adapt to the low signal to noise ratio and reduce the amount of computation greatly. These algorithms can be applied in NMR logging. 展开更多
关键词 nuclear magnetic resonance T2 spectrum singular value decomposition regularization method
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The Necessary and Sufficient Conditions for Two Kinds of Matrix Equtions Having Semipositive Subdefinite Solutions 被引量:1
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作者 何楚宁 《Chinese Quarterly Journal of Mathematics》 CSCD 2002年第4期62-68,共7页
Finding solutions of matrix equations in given set SR n×n is an active research field. Lots of investigation have done for these cases, where S are the sets of general or symmetric matrices and symmetric posit... Finding solutions of matrix equations in given set SR n×n is an active research field. Lots of investigation have done for these cases, where S are the sets of general or symmetric matrices and symmetric positive definite or sysmmetric semiposite definite matrices respectively . Recently, however, attentions are been paying to the situation for S to be the set of general(semi) positive definite matrices(called as semipositive subdefinite matrices below) . In this paper the necessary and sufficient conditions for the following two kinds of matrix equations having semipositive, subdefinite solutions are obtained. General solutions and symmetric solutions of the equations (Ⅰ) and (Ⅱ) have been considered in in detail. 展开更多
关键词 semipositive subdefinite symmetric semipositie definite generalized singualr value decomposition
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OPTIMIZATION WITH QUADRATIC CONSTRAINT IN APPLICATION OF STRUCTURE DYNAMIC MODEL UPDATING 被引量:1
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作者 桂冰 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2005年第3期212-215,共4页
A model updating optimization algorithm under quadratic constraints is applied to structure dynamic model updating. The updating problems of structure models are turned into the optimization with a quadratic constrain... A model updating optimization algorithm under quadratic constraints is applied to structure dynamic model updating. The updating problems of structure models are turned into the optimization with a quadratic constraint. Numerical method is presented by using singular value decomposition and an example is given. Compared with the other method, the method is efficient and feasible. 展开更多
关键词 updating model quadratic constraint singular value decomposition
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On the Existence of Positive Solution for n OrderSingular Boundary Value Problems 被引量:1
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作者 Shi Guoliang (Jinan School of Petrochemical Economy,Shandong,Jinan,250101) 《Chinese Quarterly Journal of Mathematics》 CSCD 1998年第3期68-73, ,共6页
In this paper,we consider the high order singular boundary value problems: u (n) (t)+a(t)f(u(t))=0, 0<t<1, u (k) (0)=u(1)=0,0kn-2. Where, a(t)∈c(0,1) and a(t)>0,t∈(0,1). a(t) may be singular at t=0,t=1. f(u... In this paper,we consider the high order singular boundary value problems: u (n) (t)+a(t)f(u(t))=0, 0<t<1, u (k) (0)=u(1)=0,0kn-2. Where, a(t)∈c(0,1) and a(t)>0,t∈(0,1). a(t) may be singular at t=0,t=1. f(u)∈c[0,+∞) and f(u)0. n is positive integer and n2. When f(u) satisfies the superlinear and sublinear conditions,we give the sufficient conditions to the existence of the positive solution. 展开更多
关键词 singular BVP SUPERLINEAR SUBLINEAR positive solution CONE
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Direct linear discriminant analysis based on column pivoting QR decomposition and economic SVD
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作者 胡长晖 路小波 +1 位作者 杜一君 陈伍军 《Journal of Southeast University(English Edition)》 EI CAS 2013年第4期395-399,共5页
A direct linear discriminant analysis algorithm based on economic singular value decomposition (DLDA/ESVD) is proposed to address the computationally complex problem of the conventional DLDA algorithm, which directl... A direct linear discriminant analysis algorithm based on economic singular value decomposition (DLDA/ESVD) is proposed to address the computationally complex problem of the conventional DLDA algorithm, which directly uses ESVD to reduce dimension and extract eigenvectors corresponding to nonzero eigenvalues. Then a DLDA algorithm based on column pivoting orthogonal triangular (QR) decomposition and ESVD (DLDA/QR-ESVD) is proposed to improve the performance of the DLDA/ESVD algorithm by processing a high-dimensional low rank matrix, which uses column pivoting QR decomposition to reduce dimension and ESVD to extract eigenvectors corresponding to nonzero eigenvalues. The experimental results on ORL, FERET and YALE face databases show that the proposed two algorithms can achieve almost the same performance and outperform the conventional DLDA algorithm in terms of computational complexity and training time. In addition, the experimental results on random data matrices show that the DLDA/QR-ESVD algorithm achieves better performance than the DLDA/ESVD algorithm by processing high-dimensional low rank matrices. 展开更多
关键词 direct linear discriminant analysis column pivoting orthogonal triangular decomposition economic singular value decomposition dimension reduction feature extraction
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An Extended Closed-loop Subspace Identification Method for Error-in-variables Systems 被引量:1
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作者 刘涛 邵诚 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2012年第6期1136-1141,共6页
A closed-loop subspace identification method is proposed for industrial systems subject to noisy input-output observations, known as the error-in-variables (EIV) problem. Using the orthogonal projection approach to el... A closed-loop subspace identification method is proposed for industrial systems subject to noisy input-output observations, known as the error-in-variables (EIV) problem. Using the orthogonal projection approach to eliminate the noise influence, consistent estimation is guaranteed for the deterministic part of such a system. A strict proof is given for analyzing the rank condition for such orthogonal projection, in order to use the principal component analysis (PCA) based singular value decomposition (SVD) to derive the extended observability matrix and lower triangular Toeliptz matrix of the plant state-space model. In the result, the plant state matrices can be retrieved in a transparent manner from the above matrices. An illustrative example is shown to demonstrate the effectiveness and merits of the proposed subspace identification method. 展开更多
关键词 closed-loop error-in-variables system subspace identification extended observability matrix orthogonal projection
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AN ALGORITHM FOR DICTIONARY GENERATION IN SPARSE REPRESENTATION
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作者 Xie Zongbo Feng Jiuchao 《Journal of Electronics(China)》 2009年第6期836-841,共6页
The K-COD (K-Complete Orthogonal Decomposition) algorithm for generating adaptive dictionary for signals sparse representation in the framework of K-means clustering is proposed in this paper,in which rank one approxi... The K-COD (K-Complete Orthogonal Decomposition) algorithm for generating adaptive dictionary for signals sparse representation in the framework of K-means clustering is proposed in this paper,in which rank one approximation for components assembling signals based on COD and K-means clustering based on chaotic random search are well utilized. The results of synthetic test and empirical experiment for the real data show that the proposed algorithm outperforms recently reported alternatives: K-Singular Value Decomposition (K-SVD) algorithm and Method of Optimal Directions (MOD) algorithm. 展开更多
关键词 Sparse representation K-Complete Orthogonal Decomposition (K-COD) Adaptivedictionary
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Existence and Multiplicity of Positive Solutions to Quasilinear Elliptic Systems Involving Multiple Hardy-Type Terms and Concave-Convex Nonlinearities
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作者 Tsing-San Hsu 《Journal of Mathematics and System Science》 2013年第3期150-161,共12页
Regular semilinear elliptic systems have been studied extensively and many conclusions have been established. However, the elliptic systems involving the Hardy inequality and concave-convex nonlinearities have seldom ... Regular semilinear elliptic systems have been studied extensively and many conclusions have been established. However, the elliptic systems involving the Hardy inequality and concave-convex nonlinearities have seldom been studied and we only find few results. Thus it is necessary for us to investigate the related singular systems deeply. In this paper, a quasilinear elliptic system is investigated, which involves multiple Hardy-type terms and concave-convex nonlinearities. To the best of our knowledge, such a problem has not been discussed. By using a variational method involving the Nehari manifold and some analytical techniques, we prove that there exist at least two positive solutions to the system. 展开更多
关键词 Quasilinear elliptic system multiple Hardy-type terms variational method Nehari manifold.
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Positive Solutions for Singular Boundary Value Problem of Fourth Order
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作者 刘嘉荃 熊明 曾平安 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2005年第4期571-581,共11页
Some existence results existence of the positive solutions for singular boundary value problems {u(4)=p(t)f(u(t)),r∈(0,1) u(0)=u(1)=0,u'(0)=u'(1)=0,are given, where the function p(t) may be sing... Some existence results existence of the positive solutions for singular boundary value problems {u(4)=p(t)f(u(t)),r∈(0,1) u(0)=u(1)=0,u'(0)=u'(1)=0,are given, where the function p(t) may be singular at t = 0, 1. 展开更多
关键词 singular boundary value problem positive solution variational method.
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Existence of Solutions to a Class of Higher-Order Singular Boundary Value Problem for One-Dimensional p-Laplacian
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作者 田玉 葛渭高 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2007年第2期282-288,共7页
This paper deals with the existence of positive solutions for the problem {(Фp(x^(n-1)(t)))′+f(t,x,…,x^(n-1)=0,0〈t〈1, x^(i)(0)=0,0≤i≤n-3, x^(n-2)(0)-B0(x^(n-1)(0))=0,x^(n-2)(1)+B1... This paper deals with the existence of positive solutions for the problem {(Фp(x^(n-1)(t)))′+f(t,x,…,x^(n-1)=0,0〈t〈1, x^(i)(0)=0,0≤i≤n-3, x^(n-2)(0)-B0(x^(n-1)(0))=0,x^(n-2)(1)+B1(x^(x-1)(1))=0, where Фp(s) = |s|^p-2s, p 〉 1. f may be singular at x^(i) = 0, i = 0,...,n- 2. The proof is based on the Leray-Schauder degree and Vitali's convergence theorem. 展开更多
关键词 singular higher-order differential equation positive solution Vitali's convergence theorem.
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