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The latest research articles published by Boundary Value Problems20150724T00:00:00Z Exponential decay rate for a quasilinear von Karman equation of memory type with acoustic boundary conditions In this paper, we show the exponential decay result of the quasilinear von Karman equation of memory type with acoustic boundary conditions. This work is devoted to investigating the influence of kernel function g and the effect of the nonlinear term

u
′

ρ
u
″
and to proving exponential decay rates of solutions when g does not necessarily decay exponentially. This result improves on earlier ones concerning the exponential decay.MSC: 35L70, 35B40, 76Exx.
http://www.boundaryvalueproblems.com/content/2015/1/122
Mi LeeJong ParkYong KangBoundary Value Problems 2015, null:12220150724T00:00:00Zdoi:10.1186/s136610150381x/content/figures/s136610150381xtoc.gifBoundary Value Problems16872770${item.volume}12220150724T00:00:00ZXML Solutions for a degenerate <inlineformula> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" name="s1366101503856i1"> <m:mi>p</m:mi> <m:mo stretchy="false">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy="false">)</m:mo> </m:math> </inlineformula>Laplacian equation with a nonsmooth potential This paper is concerned with a degenerate
p
(
x
)
Laplacian equation with a nonsmooth potential. We establish a compact embedding
W
1
,
p
(
x
)
(
ω
,
Ω
)
↪
L
q
(
x
)
(
α
(
x
)
,
Ω
)
under suitable conditions and obtain the existence and multiplicity of solutions to the degenerate
p
(
x
)
Laplacian equation by the theories of nonsmooth critical point and the variable exponent LebesgueSobolev spaces. Some recent results in the literature are generalized and improved.MSC: 35J20, 35R70, 35J25.
http://www.boundaryvalueproblems.com/content/2015/1/120
Ziqing YuanLihong HuangBoundary Value Problems 2015, null:12020150718T12:00:00Zdoi:10.1186/s1366101503856/content/figures/s1366101503856toc.gifBoundary Value Problems16872770${item.volume}12020150718T12:00:00ZXML Global and blowup solutions of semilinear heat equation involving the square root of the Laplacian In this paper, we consider nonlinear parabolic equations involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary condition. We use the method on harmonic extension to study the existence and asymptotic estimates of global solutions, as well as the blowup of the parabolic equation.MSC: 35J99, 45E10, 45G05.
http://www.boundaryvalueproblems.com/content/2015/1/121
Yongqiang XuZhong TanDaoheng SunBoundary Value Problems 2015, null:12120150718T00:00:00Zdoi:10.1186/s1366101503847/content/figures/s1366101503847toc.gifBoundary Value Problems16872770${item.volume}12120150718T00:00:00ZXML Global existence and asymptotic behavior of solutions to a semilinear parabolic equation on Carnot groups In this paper we consider the semilinear parabolic equation
∑
i
,
j
=
1
m
a
i
j
X
i
X
j
u
−
∂
t
u
+
V
u
p
=
0
with a general class of potentials
V
=
V
(
ξ
,
t
)
, where
A
=
{
a
i
j
}
i
,
j
is a positive definite symmetric matrix and the
X
i
’s denotes a system of leftinvariant vector fields on a Carnot group G. Based on a fixed point argument and by establishing some new estimates involving the heat kernel, we study the existence and largetime behavior of global positive solutions to the preceding equation.MSC: 35K65, 35J70, 35B40.
http://www.boundaryvalueproblems.com/content/2015/1/119
Zixia YuanBoundary Value Problems 2015, null:11920150716T12:00:00Zdoi:10.1186/s1366101503838/content/figures/s1366101503838toc.gifBoundary Value Problems16872770${item.volume}11920150716T12:00:00ZXML Blowup criteria of smooth solutions to the threedimensional magnetomicropolar fluid equations In this short article, the initial value problem for the 3D magnetomicropolar fluid equations is investigated. Some new blowup criteria of smooth solutions in terms of the vorticity and the velocity in a homogenous Besov space are established, respectively.MSC: 76A15, 76B03.
http://www.boundaryvalueproblems.com/content/2015/1/118
Yinxia WangBoundary Value Problems 2015, null:11820150715T12:00:00Zdoi:10.1186/s1366101503829/content/figures/s1366101503829toc.gifBoundary Value Problems16872770${item.volume}11820150715T12:00:00ZXML On the spectrum of the quadratic pencil of differential operators with periodic coefficients on the semiaxis In this paper, the spectrum and resolvent of the operator
L
λ
generated by the differential expression
ℓ
λ
(
y
)
=
y
″
+
q
1
(
x
)
y
′
+
[
λ
2
+
λ
q
2
(
x
)
+
q
3
(
x
)
]
y
and the boundary condition
y
′
(
0
)
−
h
y
(
0
)
=
0
are investigated in the space
L
2
(
R
+
)
. Here the coefficients
q
1
(
x
)
,
q
2
(
x
)
,
q
3
(
x
)
are periodic functions whose Fourier series are absolutely convergent and Fourier exponents are positive. It is shown that continuous spectrum of the operator
L
λ
consists of the interval
(
−
∞
,
+
∞
)
. Moreover, at most a countable set of spectral singularities can exists over the continuous spectrum and at most a countable set of eigenvalues can be located outside of the interval
(
−
∞
,
+
∞
)
. Eigenvalues and spectral singularities with sufficiently large modulus are simple and lie near the points
λ
=
±
n
2
,
n
∈
N
.MSC: 34L05, 47E05.
http://www.boundaryvalueproblems.com/content/2015/1/117
Ashraf OrujovBoundary Value Problems 2015, null:11720150714T12:00:00Zdoi:10.1186/s136610150380y/content/figures/s136610150380ytoc.gifBoundary Value Problems16872770${item.volume}11720150714T12:00:00ZXML Global existence and exponential stability for the strong solutions in <inlineformula> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" name="s1366101503758i1"> <m:msup> <m:mi>H</m:mi> <m:mn>2</m:mn> </m:msup> </m:math> </inlineformula> to the 3D chemotaxis model We prove the global existence of a unique strong solution to the initial boundary value problem for the 3D chemotaxis model on a bounded domain with slip boundary condition when the initial perturbation is small in
H
2
. Moreover, based on energy methods, we also prove that the strong solution converges to a steady state exponentially fast in time.
http://www.boundaryvalueproblems.com/content/2015/1/116
Yinghui ZhangWeijun XieBoundary Value Problems 2015, null:11620150710T00:00:00Zdoi:10.1186/s1366101503758/content/figures/s1366101503758toc.gifBoundary Value Problems16872770${item.volume}11620150710T00:00:00ZXML Multiple solutions for biharmonic equations with improved subcritical polynomial growth and subcritical exponential growth The main purpose of this paper is to establish the existence of three nontrivial solutions for a class of fourthorder elliptic equations with subcritical polynomial growth and subcritical exponential growth by using the minimax method and Morse theory.
http://www.boundaryvalueproblems.com/content/2015/1/115
Ruichang PeiJihui ZhangBoundary Value Problems 2015, null:11520150709T12:00:00Zdoi:10.1186/s1366101503785/content/figures/s1366101503785toc.gifBoundary Value Problems16872770${item.volume}11520150709T12:00:00ZXML A note on the boundary behavior for a modified Green function in the upperhalf space Motivated by (Xu et al. in Bound. Value Probl. 2013:262, 2013) and (Yang and Ren in Proc. Indian Acad. Sci. Math. Sci. 124(2):175178, 2014), in this paper we aim to construct a modified Green function in the upperhalf space of the ndimensional Euclidean space, which generalizes the boundary property of general Green potential.
http://www.boundaryvalueproblems.com/content/2015/1/114
Yulian ZhangValery PiskarevBoundary Value Problems 2015, null:11420150707T12:00:00Zdoi:10.1186/s136610150363z/content/figures/s136610150363ztoc.gifBoundary Value Problems16872770${item.volume}11420150707T12:00:00ZXML Existence results for hybrid fractional integrodifferential equations In this paper we study existence results for initial value problems for hybrid fractional integrodifferential equations. A couple of hybrid fixed point theorems for the sum of three operators are used for proving the main results. Examples illustrating the results are also presented.MSC: 34A08, 34A12.
http://www.boundaryvalueproblems.com/content/2015/1/113
Surang SithoSotiris NtouyasJessada TariboonBoundary Value Problems 2015, null:11320150703T12:00:00Zdoi:10.1186/s1366101503767/content/figures/s1366101503767toc.gifBoundary Value Problems16872770${item.volume}11320150703T12:00:00ZXML