the solution of second order differential equation
Báo cáo hóa học: " Research Article On the Spectrum of Almost Periodic Solution of Second-Order Neutral Delay Differential Equations with Piecewise Constant of Argument" ppt
Ngày tải lên :
21/06/2014, 20:20
... expressions of x
2n
,x
2n1
,y
2n
,ωt, and xt are important in the process of
studying the spectrum containment of the almost periodic solution of 1.1. Before giving
the main theorem, we list the ... B}.
We postpone the proof of this theorem to the next section.
3. The Proof of Main Theorem
To show the Main Theorem, we need some more lemmas.
Lemma 3.1. Let f ∈APR,thenσ
b
f
i
2n
,σ
b
f
i
2n1
,σ
b
h
2n
,σ
b
h
2n1
... ∈ R, which guarantees the uniqueness of solution of 1.1 and cannot be
omitted.
To study the spectrum of almost periodic solution of 1.1, we firstly study the solution
of 1.1.Let
f
1
n
n1
n
s
n
f
σ
dσ...
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Báo cáo toán học: " Lyapunov-type inequalities for a class of even-order differential equations" doc
Ngày tải lên :
20/06/2014, 21:20
... interval symmetrizes about the origin. Then, similar to the proof of (2.9), we
can verify the condition f
(α) = f
(β), and the other conditions in Lemma 2.2 are satisfied
all the way. Hence, it also ... contributions
QZ carried out the theoretical proof and drafted the manuscript. XH participated in the
design and coordination. Both of the two authors read and approved the final manuscript.
References
[1] ... [α, β], too. Then, by a similar
method to the proof of (2.3) together with Lemma 2.2, we can obtain (2.4) immediately.
For the other ordinary cases, i.e., a = 0, we only need to move the interval...
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Báo cáo hóa học: "Research Article Iterative Solutions of Singular Boundary Value Problems of Third-Order Differential Equation" potx
Ngày tải lên :
21/06/2014, 05:20
... and the existence results of
nontrivial solutions and positive solutions are given by means of the topological degree
theory. Motivated by the above works, we consider the singular third -order ... “Existence of solutions for a class of third -order nonlinear boundary value
problems,” Journal of Mathematical Analysis and Applications, vol. 294, no. 1, pp. 104–112, 2004.
14 D. Guo, Semi-Ordered ... problem,”
Journal of Mathematical Analysis and Applications, vol. 323, no. 1, pp. 413–425, 2006.
12 Y. Sun, “Positive solutions of singular third -order three-point boundary value problem,” Journal of
Mathematical...
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báo cáo hóa học:" Research Article Regularly Varying Solutions of Second-Order Difference Equations with Arbitrary Sign Coefficient" ppt
Ngày tải lên :
21/06/2014, 11:20
... multiple of k.
On the other hand, in the remaining two cases, the study of the regular variation of the
solutions gives the additional information that the positive solutions, even if they are ... M
RV
2
M
∞,0
.
The above theorem shows how the study of the regular variation of the solutions
and the M-classification supplement each other to give an asymptotic description of
nonoscillatory solutions. ... general equations. The aim of this section is to analyze the relations between
the classification of the eventually positive solutions according to their regularly varying
behavior, and the M-classification....
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báo cáo hóa học:" Research Article Minimal Nonnegative Solution of Nonlinear Impulsive Differential Equations on Infinite Interval" pot
Ngày tải lên :
21/06/2014, 11:20
... economics. The theory of impulsive differential equations has
become an important area of investigation in the recent years and is much richer than the
corresponding theory of differential equations. ... mentioning the works
by Guo 31.In31, Guo investigated the minimal nonnegative solution of the following
initial value problem for a second order nonlinear impulsive integrodifferential equation of
Volterra ... we will use the cone theory and
monotone iterative technique to investigate the existence of minimal nonnegative solution
for a class of second- order nonlinear impulsive differential equations on...
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- 0
báo cáo hóa học: " Study of the asymptotic eigenvalue distribution and trace formula of a second order operatordifferential equation" ppt
Ngày tải lên :
21/06/2014, 02:20
... 1+hν
2
⎤
⎥
⎦
.
(2:7)
Further , let N be the number of positive roots of the function in (2.6), and W be the
number of sign changes in its coefficients. Because the radius of convergence of this
series is ∞, then ... verified that in the vicinity of zero, the function g(z) is of order O (z
ν
).
By virtue of this asymptotic and because g(z) is an odd function, the integral along the
left-hand side of the contour ... δ >0.
Then, we can state the following theorem.
Theorem 3.2. Let the conditions of Theorem 2.1, (3.6) and (3.7) hold. If the operator-
value function q(t) has properties 1-3, then the following...
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Báo cáo hóa học: " Positive solutions of the three-point boundary value problem for fractional-order differential equations with an advanced argument" ppt
Ngày tải lên :
21/06/2014, 03:20
... fractional -order models have proved to be more accurate than integer-
order models, i.e., there are more degrees of freedom in the fractional -order models. In
consequence, the subject of fractional differential ... as an important area of investigation. For the general theory and applications of integer
order differential equations wit h deviat ed arguments, we refer the reader to the refer-
ences [39-45].
As ... mentioning that the condit ions of our theorems are easily to
verify, so they are applicable to a variety of problems, see Examples 4.1 and 4.2.
The proof of our main resul ts is based upon the following...
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báo cáo hóa học:" Research Article Biorthogonal Systems Approximating the Solution of the Nonlinear Volterra Integro-Differential Equation" doc
Ngày tải lên :
21/06/2014, 10:20
... ε
k
,
3.7
and therefore,
Tz
k−1
− z
k
≤ ε
k
3.8
as announced.
The next result is used in order to establish the fact that the sequence defined in
Theorem 3.1 approximates the solution of the nonlinear ... in order to approximate the solution of
the nonlinear Volterra integro-differential equation. We define, following a fixed-point approach,
a sequence of functions which approximate the solution of ... estimate the rate of convergence of the sequence of
projections. For this purpose, consider the dense subset {t
i
}
i≥1
of distinct points in 0, 1 and
let T
n
be the set {t
1
, ,t
n
} ordered...
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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
... 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: ... still open. The purpose of this and the next paper Error
bounds for asymptotic solutions of second- order linear difference equations II: the second
case is to estimate error bounds for solutions ... finite. Equation 3.10 is a inhomogeneous second- order linear difference equation; its
solution takes the form of a particular solution added to an arbitrary linear combination of
solutions to the...
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- xác định mức độ đáp ứng về văn hoá và chuyên môn trong ct
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