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The latest research articles published by Boundary Value Problems20150930T00:00:00Z Triple positive solutions for a second order <it>m</it>point boundary value problem with a delayed argument In this paper, we establish the new expression and properties of Green’s function for an mpoint boundary value problem with a delayed argument. Furthermore, using Hölder’s inequality and a fixed point theorem due to Leggett and Williams, the existence of at least three positive solutions is also given. We discuss our problem with a delayed argument. In this case, our results cover mpoint boundary value problems without delayed arguments and are compared with some recent results. An example is included to illustrate our main results.
http://www.boundaryvalueproblems.com/content/2015/1/178
Jie ZhouMeiqiang FengBoundary Value Problems 2015, null:17820150930T00:00:00Zdoi:10.1186/s136610150436z/content/figures/s136610150436ztoc.gifBoundary Value Problems16872770${item.volume}17820150930T00:00:00ZXML The asymptotic property for nonlinear fourthorder Schrödinger equation with gain or loss We study the Cauchy problem of the nonlinear fourthorder Schrödinger equation with gain or loss:
i
u
t
+
△
2
u
+
λ

u

α
u
+
i
ε
a
(
t
)

u

β
u
=
0
,
x
∈
R
n
,
t
∈
R
, where
2
≤
α
≤
8
n
−
4
and
2
≤
β
≤
8
n
−
4
, ε is a real number,
a
(
t
)
is a real function, and
n
>
4
. We study the asymptotic properties of its local and global solutions as
ε
→
0
.
http://www.boundaryvalueproblems.com/content/2015/1/177
Cuihua GuoBoundary Value Problems 2015, null:17720150930T00:00:00Zdoi:10.1186/s1366101504421/content/figures/s1366101504421toc.gifBoundary Value Problems16872770${item.volume}17720150930T00:00:00ZXML On global behavior of weak solutions to the NavierStokes equations of compressible fluid for <inlineformula> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" name="s1366101504430i1"> <m:mi>γ</m:mi> <m:mo>=</m:mo> <m:mn>5</m:mn> <m:mo stretchy="false">/</m:mo> <m:mn>3</m:mn> </m:math> </inlineformula> In this article, we consider the global behavior of weak solutions of the NavierStokes equations of a compressible fluid in a bounded domain driven by bounded forces for the adiabatic constant
γ
=
5
/
3
. Under the condition of a small mass depending on the given forces, we prove the existence of bounded absorbing sets of weak solutions, and thus we further get global bounded trajectories and global attractors to the weak solutions.MSC: 35B40, 35B41, 76N99.
http://www.boundaryvalueproblems.com/content/2015/1/176
Xiaoying WangWeiwei WangBoundary Value Problems 2015, null:17620150929T00:00:00Zdoi:10.1186/s1366101504430/content/figures/s1366101504430toc.gifBoundary Value Problems16872770${item.volume}17620150929T00:00:00ZXML Positive periodic solutions for second order differential equations with impulsive effects The existence of positive periodic solutions for a class of second order impulsive differential equations is studied. By using a fixed point theorem in cone, we obtain two existence results, which extend some known results.MSC: 34B18, 34B37.
http://www.boundaryvalueproblems.com/content/2015/1/175
Weibing WangXuxin YangBoundary Value Problems 2015, null:17520150928T00:00:00Zdoi:10.1186/s1366101504341/content/figures/s1366101504341toc.gifBoundary Value Problems16872770${item.volume}17520150928T00:00:00ZXML Passivity analysis of spatially and temporally BAM neural networks with the Neumann boundary conditions In the paper, a delaydifferential equation modeling a bidirectional associative memory neural networks (BAM NNs) with reactiondiffusion terms is investigated, for which the input and output variables are varied with the time and space variables. By taking advantage of the inequality techniques, some LyapunovKrasovskii functional candidates are introduced to arrive at the novel sufficient conditions that warrant the passivity of spatially and temporally BAM NNs with mixed time delays. Moreover, when the parameter uncertainties appear in spatially and temporally BAM NNs, the criterion for robust passivity is also given. Novel passivity criteria are proposed in terms of inequalities, which can be checked easily. A numerical example is provided to demonstrate the effectiveness of the proposed results.
http://www.boundaryvalueproblems.com/content/2015/1/174
Weiyuan ZhangBoundary Value Problems 2015, null:17420150925T12:00:00Zdoi:10.1186/s1366101504350/content/figures/s1366101504350toc.gifBoundary Value Problems16872770${item.volume}17420150925T12:00:00ZXML Inverse problem for nonstationary system of magnetohydrodynamics We study the inverse problem for nonstationary system of magnetic hydrodynamics in which it is required to determine the velocity of the fluid
v
→
(
x
,
t
)
, the magnetic tension
H
→
(
x
,
t
)
, the pressure gradient
∇
p
(
x
,
t
)
, but also the external forces
f
→
(
x
)
and the current
rot
j
→
(
x
)
. In this case, to the conditions constituting the direct problem are added additional conditions. The trace speed, the magnetic tension, and the pressure gradient in the final moment, time
t
=
T
, are taken as additional information. The strong generalized solvability of the inverse problem in the twodimensional case is proved.
http://www.boundaryvalueproblems.com/content/2015/1/173
Undasin AbylkairovSerik AitzhanovBoundary Value Problems 2015, null:17320150923T12:00:00Zdoi:10.1186/s136610150438x/content/figures/s136610150438xtoc.gifBoundary Value Problems16872770${item.volume}17320150923T12:00:00ZXML Monotone positive solution of a fourthorder BVP with integral boundary conditions In this paper, we investigate the existence of concave and monotone positive solutions for a nonlinear fourthorder differential equation with integral boundary conditions of the form
x
(
4
)
(
t
)
=
f
(
t
,
x
(
t
)
,
x
′
(
t
)
,
x
″
(
t
)
)
,
t
∈
[
0
,
1
]
,
x
(
0
)
=
x
′
(
1
)
=
x
‴
(
1
)
=
0
,
x
″
(
0
)
=
∫
0
1
g
(
s
)
x
″
(
s
)
d
s
, where
f
∈
C
(
[
0
,
1
]
×
[
0
,
+
∞
)
2
×
(
−
∞
,
0
]
,
[
0
,
+
∞
)
)
,
g
∈
C
(
[
0
,
1
]
,
[
0
,
+
∞
)
)
. By using a fixed point theorem of cone expansion and compression of norm type, the existence and nonexistence of concave and monotone positive solutions for the above boundary value problems is obtained. Meanwhile, as applications of our results, some examples are given.MSC: 34B15, 34B18.
http://www.boundaryvalueproblems.com/content/2015/1/172
Xuezhe LvLibo WangMinghe PeiBoundary Value Problems 2015, null:17220150922T12:00:00Zdoi:10.1186/s1366101504412/content/figures/s1366101504412toc.gifBoundary Value Problems16872770${item.volume}17220150922T12:00:00ZXML Quasilinear elliptic equations with Hardy terms and HardySobolev critical exponents: nontrivial solutions In this paper, we obtain one positive solution and two nontrivial solutions of a quasilinear elliptic equation with pLaplacian, Hardy term and HardySobolev critical exponent by using variational methods and some analysis techniques. In particular, our results extend some existing ones.MSC: 35B33, 35J60.
http://www.boundaryvalueproblems.com/content/2015/1/171
Guanwei ChenBoundary Value Problems 2015, null:17120150922T12:00:00Zdoi:10.1186/s1366101504403/content/figures/s1366101504403toc.gifBoundary Value Problems16872770${item.volume}17120150922T12:00:00ZXML The local wellposedness and stability to a nonlinear generalized DegasperisProcesi equation A nonlinear generalized DegasperisProcesi equation is investigated. The local wellposedness of a strong solution for the equation in the Sobolev space
H
s
(
R
)
with
s
>
3
2
is established. The
L
1
(
R
)
stability is obtained under certain assumptions on the initial data.MSC: 35G25, 35L05.
http://www.boundaryvalueproblems.com/content/2015/1/170
Jing ChenRui LiBoundary Value Problems 2015, null:17020150918T12:00:00Zdoi:10.1186/s1366101504332/content/figures/s1366101504332toc.gifBoundary Value Problems16872770${item.volume}17020150918T12:00:00ZXML Stabilization of a laminated beam with interfacial slip by boundary controls We consider two identical beams on top of each other with an adhesive in between. A considerable natural slip occurs in the structure and will not be ignored as was done in the previous investigations. In this work we take into account this slip and prove that we can stabilize the system in an exponential manner using boundary controls. The model consists of three coupled equations. The first two are related to the wellknown Timoshenko system, and the third one describes the dynamic of the slip. Our result improves the few existing similar works in the literature.MSC: 34B05, 34D05, 34H05.
http://www.boundaryvalueproblems.com/content/2015/1/169
NasserEddine TatarBoundary Value Problems 2015, null:16920150918T00:00:00Zdoi:10.1186/s1366101504323/content/figures/s1366101504323toc.gifBoundary Value Problems16872770${item.volume}16920150918T00:00:00ZXML