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学者姓名：江良平
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| GB/T 7714 | Shen, M. , Jiang, L. P. . Oscillating dark energy model in plane symmetric space-time with time periodic varying deceleration parameter (vol 354, pg 607, 2014) [J]. | ASTROPHYSICS AND SPACE SCIENCE , 2015 , 356 (2) : 413-413 . |
| MLA | Shen, M. 等. "Oscillating dark energy model in plane symmetric space-time with time periodic varying deceleration parameter (vol 354, pg 607, 2014)" . | ASTROPHYSICS AND SPACE SCIENCE 356 . 2 (2015) : 413-413 . |
| APA | Shen, M. , Jiang, L. P. . Oscillating dark energy model in plane symmetric space-time with time periodic varying deceleration parameter (vol 354, pg 607, 2014) . | ASTROPHYSICS AND SPACE SCIENCE , 2015 , 356 (2) , 413-413 . |
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In this paper, an oscillating dark energy model is presented in an isotropic but inhomogeneous plane symmetric space-time by considering a time periodic varying deceleration parameter. We find three different types of new solutions which describe different scenarios of oscillating universe. The first two solutions show an oscillating universe with singularities. For the third one, the universe is singularity-free during the whole evolution. Moreover, the Hubble parameter oscillates and keeps positive which explores an interesting possibility to unify the early inflation and late time acceleration of the universe.
Keyword ：
Dark energy Dark energy Deceleration parameter Deceleration parameter Oscillating universe Oscillating universe Plane symmetric Plane symmetric
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| GB/T 7714 | She, M. , Jiang, L. P. . Oscillating dark energy model in plane symmetric space-time with time periodic varying deceleration parameter [J]. | ASTROPHYSICS AND SPACE SCIENCE , 2014 , 354 (2) : 607-610 . |
| MLA | She, M. 等. "Oscillating dark energy model in plane symmetric space-time with time periodic varying deceleration parameter" . | ASTROPHYSICS AND SPACE SCIENCE 354 . 2 (2014) : 607-610 . |
| APA | She, M. , Jiang, L. P. . Oscillating dark energy model in plane symmetric space-time with time periodic varying deceleration parameter . | ASTROPHYSICS AND SPACE SCIENCE , 2014 , 354 (2) , 607-610 . |
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The classical criterion of asymptotic stability of the zero solution of equations x′ = f(t, x) is that there exists a function V (t, x), a({double pipe}x{double pipe}) ≤ V (t, x) ≤ b({double pipe}x{double pipe}) for some a, b ∈ K such that V(t, x) ≤ -c({double pipe}x{double pipe}) for some c ∈ K. In this paper, we prove that if V (t, x) is bounded on some set [tk - T, tk + T] × BH(tk → +∞ as k → ∞), then the condition that V(t, x) ≤ -c({double pipe}x{double pipe}) can be weakened and replaced by that, for some c′ ∈ K. Moreover, the author also presents a corresponding instability criterion. [1-10] © 2011 Springer Science+Business Media, Inc.
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| GB/T 7714 | Jiang, L. . Asymptotic stability and instability criteria for nonautonomous systems [J]. | Journal of Mathematical Sciences , 2011 , 177 (3) : 395-401 . |
| MLA | Jiang, L. . "Asymptotic stability and instability criteria for nonautonomous systems" . | Journal of Mathematical Sciences 177 . 3 (2011) : 395-401 . |
| APA | Jiang, L. . Asymptotic stability and instability criteria for nonautonomous systems . | Journal of Mathematical Sciences , 2011 , 177 (3) , 395-401 . |
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本文在对二分性函数a(t)有适当的要求的条件下将Palmer线性化定理推广到线性部分只具有广义指数型二分性的系统,并在一定条件下证明了等价函数的强一致连续性.
Keyword ：
广义指数型二分性 广义指数型二分性 (强)拓扑等价 (强)拓扑等价 (强)等价函数 (强)等价函数
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| GB/T 7714 | 江良平 . Palmer线性化定理的一个推广 [J]. | 应用数学 , 2011 , 24 (1) : 150-157 . |
| MLA | 江良平 . "Palmer线性化定理的一个推广" . | 应用数学 24 . 1 (2011) : 150-157 . |
| APA | 江良平 . Palmer线性化定理的一个推广 . | 应用数学 , 2011 , 24 (1) , 150-157 . |
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Suppose that f(t, x) <= psi(t), integral(+infinity)(-infinity) psi(t)dt < +infinity, vertical bar f(t, x(1)) - f(t, x(2))vertical bar <= r(t)vertical bar x(1) - x(2)vertical bar, integral(+infinity)(-infinity) r(t)dt < C (C is some constant). Then if system x' = A(t)x has an ordinary dichotomy, then x' = A(t)x + f(t, x) is topologically equivalent to x' = A(t)x. If system x' = A(t)x has an ordinary dichotomy with asymptotically stable manifolds, then x' = A(t)x + f(t, x) is strongly topologically equivalent to x' = A(t)x. x' = f(t, x) can be considered as a perturbation of the linear system x' = 0, which has an ordinary dichotomy. The structure of the solution set of x' = f(t, x) is clear since x' = f(t, x) is strongly topologically equivalent to x' = 0. (C) 2008 Elsevier Ltd. All rights reserved.
Keyword ：
Ordinary dichotomy Ordinary dichotomy (Strongly)Equivalent function (Strongly)Equivalent function (Strongly)Topologically equivalent (Strongly)Topologically equivalent
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| GB/T 7714 | Jiang, Liangping . Ordinary dichotomy and global linearization [J]. | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS , 2009 , 70 (7) : 2722-2730 . |
| MLA | Jiang, Liangping . "Ordinary dichotomy and global linearization" . | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 70 . 7 (2009) : 2722-2730 . |
| APA | Jiang, Liangping . Ordinary dichotomy and global linearization . | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS , 2009 , 70 (7) , 2722-2730 . |
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The classical criterion of asymptotic stability of the zero solution of equations x' = f (t, x) is that there exists a function V(t, x), a(parallel to x parallel to) <= V(t, x) <= b(parallel to x parallel to) for some a, b is an element of K, such that V(t, x) <= -c(parallel to x parallel to) for some c is an element of K. In this paper we prove that if f(t, x) is bounded, (t, x) is uniformly continuous and bounded, then the condition that V(t, x) <= -c(parallel to x parallel to) can be weakened and replaced by V(t, x) <= 0 and {(t, x): x not equal 0, V(t, x) = 0} contains no complete trajectory of x' = f (t, x), t is an element of [-T, T], where V(t, x) = lim(k ->infinity) V(t + t(k), x), f(t, x) = lim(k ->infinity) f (t + t(k), x) uniformly for (t, x) is an element of [-T T] x B-H. (c) 2006 Elsevier Inc. All rights reserved.
Keyword ：
asymptotic stability asymptotic stability Barbashin-Krasovski theorem Barbashin-Krasovski theorem Lyapunov's direct method Lyapunov's direct method
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| GB/T 7714 | Jiang, Liangping . A generalization of Barbashin-Krasovski theorem [J]. | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2007 , 326 (2) : 1379-1382 . |
| MLA | Jiang, Liangping . "A generalization of Barbashin-Krasovski theorem" . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 326 . 2 (2007) : 1379-1382 . |
| APA | Jiang, Liangping . A generalization of Barbashin-Krasovski theorem . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2007 , 326 (2) , 1379-1382 . |
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It has been proved that if x' = A (t)x has a generalized exponential dichotomy and f (t, x) satisfies certain conditions, then the nonlinear system x' = A (t)x + f (t, x) is topologically equivalent to its linear system x' = A (t)x. In this paper, we prove that if the condition \A (t)\ <= M . a (t) is added, then x' = A (t)x + f(t, x) is strongly topologically equivalent to x' = A (t)x, where M is some positive number and a (t) is the eigenfunction of the generalized exponential dichotomy, and therefore the corresponding solutions of x' = A (t)x + f (t, x) and x' = A (t)x have the same stability. (c) 2006 Elsevier Ltd. All rights reserved.
Keyword ：
generalized exponential dichotomy generalized exponential dichotomy (strongly) equivalent function (strongly) equivalent function (strongly) topologically equivalent (strongly) topologically equivalent
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| GB/T 7714 | Jiang, Liangping . Strongly topological linearization with generalized exponential dichotomy [J]. | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS , 2007 , 67 (4) : 1102-1110 . |
| MLA | Jiang, Liangping . "Strongly topological linearization with generalized exponential dichotomy" . | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 67 . 4 (2007) : 1102-1110 . |
| APA | Jiang, Liangping . Strongly topological linearization with generalized exponential dichotomy . | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS , 2007 , 67 (4) , 1102-1110 . |
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Hartman's linearization theorem says that if all eigenvalues of matrix A have no zero real part and f(x) is small Lipschitzian, then nonlinear system x' = Ax + f (x) and its linear system x' = Ax are topologically equivalent. In 1970s Palmer extended the theorem to nonautonomous systerns. In this paper we extend Hartman's theorem to the systems with generalized exponential dichotomy. (c) 2005 Elsevier Inc. All rights reserved.
Keyword ：
generalized exponential dichotomy generalized exponential dichotomy (Strongly)equivalent function (Strongly)equivalent function (Strongly)topologically equivalent (Strongly)topologically equivalent
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| GB/T 7714 | Jiang, LP . Generalized exponential dichotomy and global linearization [J]. | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2006 , 315 (2) : 474-490 . |
| MLA | Jiang, LP . "Generalized exponential dichotomy and global linearization" . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 315 . 2 (2006) : 474-490 . |
| APA | Jiang, LP . Generalized exponential dichotomy and global linearization . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2006 , 315 (2) , 474-490 . |
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The classical criterion of asymptotic stability of the zero solution of equations x' = f(t,x) is that there exists a positive definite function V which has infinitesimal upper bound such that dV/dt is negative definite. In this paper we prove that if d(m+1)V/dt(m+1) is bounded then the condition that dV/dt is negative definite can be weakened and replaced by that dV/dt less than or equal to 0 and -(\dV/dt\ + \d(2)V/dt(2)\ + ... + \d(m)V/dt(m)\ + \d(m+p)V/dt(m+p)\) is negative definite. (C) 2004 Elsevier Inc. All rights reserved.
Keyword ：
asymptotic stability asymptotic stability instability instability Lyapunov's direct method Lyapunov's direct method
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| GB/T 7714 | Jiang, LP . On the asymptotic stability of equilibrium [J]. | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2005 , 301 (2) : 378-383 . |
| MLA | Jiang, LP . "On the asymptotic stability of equilibrium" . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 301 . 2 (2005) : 378-383 . |
| APA | Jiang, LP . On the asymptotic stability of equilibrium . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2005 , 301 (2) , 378-383 . |
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通过数学分析的技巧并构造反例, 证明了存在实数δ>0, 使得当r∈(-δ, δ)时, ∫r0∫t10∫t20…∫t2n-10f(t1, t3, …, t2n-1)f(t2, t4, …, t2n)dt2ndt2n-1…dt1≥0成立的充分必要条件是f(0)≠0.
Keyword ：
多元函数 多元函数 多重积分 多重积分 积分不等式 积分不等式
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| GB/T 7714 | 江良平 . 一类积分不等式成立的条件 [J]. | 福州大学学报(自然科学版) , 2002 , 30 (4) : 455-457 . |
| MLA | 江良平 . "一类积分不等式成立的条件" . | 福州大学学报(自然科学版) 30 . 4 (2002) : 455-457 . |
| APA | 江良平 . 一类积分不等式成立的条件 . | 福州大学学报(自然科学版) , 2002 , 30 (4) , 455-457 . |
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