... be applied to concrete partial differential equations.
1. Introduction
Of concern is the exponential stability of two coupled second- order evolution equations one
is an integro-differential equation ... properly cited.
By using the multiplier technique, we prove that the energy of a system of two coupled second
order evolution equations one is an integro-differential equation decays exponentially ... Article
Exponential Stability of Two Coupled
Second- Order Evolution Equations
Qian Wan and Ti-Jun Xiao
Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences,
Fudan...
... equal
to I. The proof of uniqueness is complete.
To prove the existence we note, first of all, that it suffices to provide a
proof if one of the κ
i
’s is equal to ±1 and one of the δ
j
’s is equal ... for all k ∈ Z. The proof of the first part of
Theorem 4.9 is complete.
In order to prove Theorem 4.9(ii), we need to compare the first and the
third factors of the two sides of (4.7). The first factors ... solutions of
isomonodromy problems for such systemsof difference equations. In the case
of one-interval gap probability this has been done (in a different language) in
[Bor], [BB]. One example of the...
... polynomial solutions of a class of linear differentialequationsof the second order. Bull A M S. 36,
77–84 (1930). doi:10.1090/S0002-9904-1930-04888-0
Azad et al. Advances in Difference Equations 2011, ... which is an
eigenfunction of L.
Specializing to second- orderequations because of their importance in applications–
and leaving in this article the higher -order case because of its technical complexity–the
canonical ... Advances in Difference Equations 2011, 2011:58
http://www.advancesindifferenceequations.com/content/2011/1/58
Page 6 of 12
3 Canonical forms of self-adjoint second- orderequations with polynomial
coefficients
Let...
... second example, we will obtain the
bound of the solutions of an integral equation.
For the sake of proving the global existence of solutions ofdifferential equations, we
first recall some basic ... in order to illustrate the validity of the
above results. In the first example, we will try to prove the global existence of the solu-
tions of a delay differential equation, while in the second ... integral equation, differential equa-
tion, bounded
1 Introduction
During the past decades, with the development of the theory ofdifferential and integral
equations, a lot of integral inequalities,...
... Article
Approximation of Solutions for Second- Order
m-Point Nonlocal Boundary Value Problems via
the Method of Generalized Quasilinearization
Ahmed Alsaedi
Department of Mathematics, Faculty of Science, ... Zuo, “On monotone method for first and secondorder periodic boundary
value problems and periodic solutions of functional differential equations, ” Journal of Mathematical
Analysis and Applications, ... the method of generalized quasilinearization to obtain a
sequence of approximate solutions converging monotonically and quadratically to a unique
solution of the following second- order m−point...
... oscillation of solutions of first order delay
difference equations, ” Cubo, vol. 7, no. 2, pp. 223–236, 2005.
14 R. Medina and M. Pituk, “Nonoscillatory solutions of a second- order difference equation of ... derived for all the solutions being
oscillating for a class of linear second- order delayed-discrete equations.
We consider the delayed second- order linear discrete equation
Δx
n
−p
n
x
n ... Article
Oscillation of Solutions of a Linear Second- Order
Discrete-Delayed Equation
J. Ba
ˇ
stinec,
1
J. Dibl
´
ık,
1, 2
and Z.
ˇ
Smarda
1
1
Department of Mathematics, Faculty of Electrical Engineering...
... Article
Multiple Positive Solutions of a Singular
Emden-Fowler Type Problem for Second- Order
Impulsive Differential Systems
Eun Kyoung Lee and Yong-Hoon Lee
Department of Mathematics, Pusan National ... 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, ... Liu, L. 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...
... questions of solvability of basic boundary value problems
for quasilinear degenerate and nonuniformly elliptic and parabolic equationsofsecond order, and
also to the investigation ofdifferential ... with this, one of
the first questions of the general theory of boundary value problems for quasilinear
elliptic equationsof the form (1)is the question of distinguishing classes of
equations for ... the proof of an a priori estimate of the Hdlder norm IIulIc^(u) for
solutions of uniformly elliptic equations.
V. The estimate of maxnl vul for equations with structure
described in terms of the...
... 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 ... non-trivial.
Although the proof of the first part of Theorem 1.2 is very similar to the
proof of Theorem 1.1, for readers’ convenience, we give its complete proof.
Lemma 3.3 Under the conditions of Theorem 1.2,...