system of two second order linear differential equations
báo cáo hóa học:" Research Article Error Bounds for Asymptotic Solutions of Second-Order Linear Difference Equations II: The First Case" pot
Ngày tải lên :
21/06/2014, 11:20
... solutions of
second- order linear difference equations II: the second case is dedicated to the case when
k<0.
1.1. The Result in [3] When k 1
When k 1, from 3 we know that 1.2 has two linearly ... completed the estimate of the error bounds for asymptotic solutions to second
order linear difference equations in the first case. For the second case, we leave it to the second
part of this paper: Error ... second- order linear difference equations, ” Journal of
Computational and Applied Mathematics, vol. 41, no. 1-2, pp. 65–94, 1992.
3 R. Wong and H. Li, “Asymptotic expansions for second- order linear...
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Báo cáo hoa học: " Research Article On Connection between Second-Order Delay Differential Equations and Integrodifferential Equations with Delay" pdf
Ngày tải lên :
21/06/2014, 20:20
... Difference Equations
Volume 2010, Article ID 143298, 8 pages
doi:10.1155/2010/143298
Research Article
On Connection between Second- Order Delay
Differential Equations and Integrodifferential
Equations ... obtained by transforming second- order delay dierential equations
ăxtat xgt btxht 0 to first -order differential equations.
1. Introduction and Preliminaries
The second order delay dierential equation
ăx
t
... defined by 2.5.
Proof. In the proof we will use notation defined in the proof of Theorem 2.1. The existence
and uniqueness of a solution of 1.11, 2.1 is a consequence of Theorem 2.1. Thus,...
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Báo cáo hóa học: " Research Article Sturm-Picone Comparison Theorem of Second-Order Linear Equations on Time Scales" ppt
Ngày tải lên :
21/06/2014, 20:20
... theorem of solution for second order nonlinear differential
equations, ” Annals of Differential Equations, vol. 19, no. 3, pp. 480–486, 2003.
7 R K. Zhuang and H W. Wu, “Sturm comparison theorem of ... theorem of second- order differential equations see Section 1.
Remark 3.6. In the discrete case: μt ≡ 1. This result is the same as Sturm comparison theorem
of second- order difference equations ... of second- order linear equations on time
scales. We first establish Picone identity on time scales and obtain our main result by using it.
Also, our result unifies the existing ones of second- order...
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báo cáo hóa học:" Research Article Limit Properties of Solutions of Singular Second-Order Differential Equations" doc
Ngày tải lên :
21/06/2014, 20:20
... Article
Limit Properties of Solutions of Singular
Second- Order Differential Equations
Irena Rach
˚
unkov
´
a,
1
Svatoslav Stan
ek,
1
Ewa Weinm
ă
uller,
2
and Michael Zenz
2
1
Department of Mathematical ... the
solvability of nonlinear singular equations subject to different types of boundary conditions.
In this section, we utilize Theorem 4.1 to show the existence of solutions for periodic
problems. The rest of ... sufficient conditions for the existence of at least
one solution of problem 5.1a and 5.1b with a>0. In the proof of this theorem, we work
also with auxiliary two- point boundary conditions:
u
0
...
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Báo cáo hóa học: " Research Article Global Behavior of Solutions to Two Classes of Second-Order Rational Difference Equations Sukanya Basu and Orlando Meri" docx
Ngày tải lên :
21/06/2014, 20:20
... Article
Global Behavior of Solutions to Two Classes of
Second- Order Rational Difference Equations
Sukanya Basu and Orlando Merino
Department of Mathematics, University of Rhode Island, Kingston, ... Dynamics of Second Order Rational Difference Equations, Chapman &
Hall/CRC, Boca Raton, Fla, USA, 2002.
2 G. Ladas, “Invariants for generalized Lyness equations, ” Journal of Difference Equations ... about the global dynamics of 1.11 and 1.13, such as
the character of the prime period -two solutions to either equation, or even for more general
rational second- order equations, when such solutions...
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galois theory of linear differential equations - m. van der put, m. singer
Ngày tải lên :
31/03/2014, 15:56
... translates into Z
L
=(r
a,b
)G
L
. A proof of Lemma 1.29 finishes
the proof of the theorem. ✷
Proof of lemma 1.29.
The proof is rather similar to the one of lemma 1.23. The only thing that we
have ... as a group of matrices
and has the structure of a linear algebraic group, that is, it is a group of invertible
matrices defined by the vanishing of a set of polynomials on the entries of these
matrices. ... O-submodules N
1
,N
2
of N with N = N
1
⊕N
2
and N
i
= F
i
for i =1, 2.
Proof. The proof is similar to the proof of Proposition 3.17. Let S
1
and S
2
be the set of eigenvalues of E acting on F
1
and...
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báo cáo hóa học:" Research Article Multiple Positive Solutions of a Singular Emden-Fowler Type Problem for Second-Order Impulsive Differential Systems" pdf
Ngày tải lên :
21/06/2014, 11:20
... Hu, and Y. Wu, “Positive solutions of two- point boundary value problems for systems
of nonlinear second- order singular and impulsive differential equations, ” Nonlinear Analysis: Theory,
Methods ... S. G. Hristova and D. D. Ba
˘
ınov, “Existence of periodic solutions of nonlinear systems of differential
equations with impulse effect,” Journal of Mathematical Analysis and Applications, vol. ... 3-4, pp. 307–
328, 2004.
4 B. Liu and J. Yu, “Existence of solution of m-point boundary value problems of second- order
differential systems with impulses,” Applied Mathematics and Computation,...
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Báo cáo sinh học: " Research Article Existence and Lyapunov Stability of Periodic Solutions for Generalized Higher-Order Neutral Differential Equations" potx
Ngày tải lên :
21/06/2014, 16:20
... Journal of Mathematical Analysis and Applications, vol. 326, no. 2, pp. 1161–1173,
2007.
9 J. Wu and Z. Wang, Two periodic solutions of second- order neutral functional differential
equations, ” ... Journal of Mathematical Analysis and Applications, vol. 329, no. 1, pp. 677–689, 2007.
10 M. R. Zhang, “Periodic solutions of linear and quasilinear neutral functional-differential equations, ”
Journal ... and Lyapunov Stability of
Periodic Solutions for Generalized Higher -Order
Neutral Differential Equations
Jingli Ren,
1
Wing-Sum Cheung,
2
and Zhibo Cheng
1
1
Department of Mathematics, Zhengzhou...
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Báo cáo sinh học: " Research Article Multiple Positive Solutions of Fourth-Order Impulsive Differential Equations with Integral Boundary Conditions and One-Dimensional p-Laplacian" ppt
Ngày tải lên :
21/06/2014, 16:20
... introduction of the basic theory of impulsive
differential equations, see Lakshmikantham et al. 1; for an overview of existing results and
of recent research areas of impulsive differential equations, ... Differential Equations, vol. 14, World Scientific,
Singapore, 1995.
6 J. Yan, “Existence of positive periodic solutions of impulsive functional differential equations with
two parameters,” Journal of Mathematical ... olution
yt,t∈ J with property 3.17.
Proof. The proof is similar to that of Theorem 3. 2of 6.
Theorem 3.5. Assume that H
1
, H
2
, 3.1 of H
3
and 3.14 and 3.15 of H
4
hold. In
addition,...
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Báo cáo sinh học: "Homoclinic solutions of some second-order non-periodic discrete systems" ppt
Ngày tải lên :
18/06/2014, 22:20
... is just the repetition of the proof of
Lemma 3.2, we omit the details of its proof.
With the aid of above preparations, now we will give the proof of Theorem
1.2.
Proof of Theorem 1.2 By(1.8), ... is in some way a type of the best expressive way of the structure of
the solution space for recurrence relations occurring in the study of second-
order linear differential equations. So, (1.3) ... similar to the proof of Lemma 3.1, so
we omit the details of its proof.
Lemma 3.4 Under the conditions of Theorem 1.2, F (x) satisfies the PS
condition.
Proof From the proof of Lemma 3.2, we see...
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báo cáo hóa học:" Homoclinic solutions of some second-order non-periodic discrete systems" doc
Ngày tải lên :
20/06/2014, 04:20
... is just the repetition of the proof of
Lemma 3.2, we omit the details of its proof.
With the aid of above preparations, now we will give the proof of Theorem
1.2.
Proof of Theorem 1.2 By(1.8), ... similar to the proof of Lemma 3.1, so
we omit the details of its proof.
Lemma 3.4 Under the conditions of Theorem 1.2, F (x) satisfies the PS
condition.
Proof From the proof of Lemma 3.2, we see ... is in some way a type of the best expressive way of the structure of
the solution space for recurrence relations occurring in the study of second-
order linear differential equations. So, (1.3)...
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