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The latest research articles published by Boundary Value Problems20141219T12:00:00ZClassical solutions for the CahnHilliard equation with decayed mobilityWe consider the CahnHilliard equation with concentration dependent mobility in two dimensions. Global existence and uniqueness of classical solutions are established for a mobility with some delayed structure and general potential including
−
u
+
γ
u
3
for both
γ
>
0
and
γ
<
0
.
http://www.boundaryvalueproblems.com/content/2014/1/264
Rui HuangMing MeiJingxue YinBoundary Value Problems 2014, null:26420141219T12:00:00Zdoi:10.1186/s1366101402646/content/figures/s1366101402646toc.gifBoundary Value Problems16872770${item.volume}26420141219T12:00:00ZXMLSolvability and positive solution of a system of secondorder boundary value problem with integral boundary conditionsThe main purpose of this paper is to establish the existence, uniqueness and positive solution of a system of secondorder boundary value problem with integral conditions. Using Banach’s fixed point theorem and the LeraySchauder nonlinear alternative, we discuss the existence and uniqueness solution of this problem, and we apply GuoKrasnoselskii’s fixed point theorem in cone to study the existence of positive solution. We also give some examples to illustrate our results.
http://www.boundaryvalueproblems.com/content/2014/1/262
Rochdi JebariAbderrahman BoukrichaBoundary Value Problems 2014, null:26220141216T12:00:00Zdoi:10.1186/s1366101402628/content/figures/s1366101402628toc.gifBoundary Value Problems16872770${item.volume}26220141216T12:00:00ZXMLA positive fixed point theorem with applications to systems of Hammerstein integral equationsWe present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of positive solutions for systems of nonlinear Hammerstein integral equations. An example is also presented to show the applicability of our results.MSC:47H10, 34B10, 34B18, 45G15, 47H30.
http://www.boundaryvalueproblems.com/content/2014/1/254
Alberto CabadaJosé CidGennaro InfanteBoundary Value Problems 2014, null:25420141211T00:00:00Zdoi:10.1186/s1366101402548/content/figures/s1366101402548toc.gifBoundary Value Problems16872770${item.volume}25420141211T00:00:00ZXMLAsymptotics of solutions of second order parabolic equations near conical points and edgesThe authors consider the first boundary value problem for a second order parabolic equation with variable coefficients in a domain with conical points or edges. In the first part of the paper, they study the Green function for this problem in the domain
K
×
R
n
−
m
, where K is an infinite cone in
R
m
,
2
≤
m
≤
n
. They obtain the asymptotics of the Green function near the vertex (
n
=
m
) and edge (
n
>
m
), respectively. This result is applied in the second part of the paper, which deals with the initialboundary value problem in this domain. Here, the righthand side f of the differential equation belongs to a weighted
L
p
space. At the end of the paper, the initialboundary value problem in a bounded domain with conical points or edges is studied.
http://www.boundaryvalueproblems.com/content/2014/1/252
Vladimir KozlovJürgen RossmannBoundary Value Problems 2014, null:25220141211T00:00:00Zdoi:10.1186/s136610140252x/content/figures/s136610140252xtoc.gifBoundary Value Problems16872770${item.volume}25220141211T00:00:00ZXMLNonlocal Hadamard fractional integral conditions for nonlinear RiemannLiouville fractional differential equationsIn this paper, we introduce a new class of boundary value problems consisting of a fractional differential equation of RiemannLiouville type,
D
q
R
L
x
(
t
)
=
f
(
t
,
x
(
t
)
)
,
t
∈
[
0
,
T
]
, subject to the Hadamard fractional integral conditions
x
(
0
)
=
0
,
x
(
T
)
=
∑
i
=
1
n
α
i
H
I
p
i
x
(
η
i
)
. Existence and uniqueness results are obtained by using a variety of fixed point theorems. Examples illustrating the results obtained are also presented.MSC:34A08, 34B15.
http://www.boundaryvalueproblems.com/content/2014/1/253
Jessada TariboonSotiris NtouyasWeerawat SudsutadBoundary Value Problems 2014, null:25320141209T12:00:00Zdoi:10.1186/s1366101402539/content/figures/s1366101402539toc.gifBoundary Value Problems16872770${item.volume}25320141209T12:00:00ZXMLSome existence theorems for fractional integrodifferential equations and inclusions with initial and nonseparated boundary conditionsIn this paper, we study the existence of solutions for a new class of boundary value problems of nonlinear fractional integrodifferential equations and inclusions of arbitrary order with initial and nonseparated boundary conditions. In the case of inclusion, the existence results are obtained for convex as well as nonconvex multifunctions. Our results rely on the standard tools of fixed point theory and are well illustrated with the aid of examples.
http://www.boundaryvalueproblems.com/content/2014/1/249
Bashir AhmadAhmed AlsaediSayyedeh NazemiShahram RezapourBoundary Value Problems 2014, null:24920141209T12:00:00Zdoi:10.1186/s1366101402495/content/figures/s1366101402495toc.gifBoundary Value Problems16872770${item.volume}24920141209T12:00:00ZXMLOn the solutions and conservation laws of the coupled DrinfeldSokolovSatsumaHirota systemIn this paper we study the coupled DrinfeldSokolovSatsumaHirota system, which was developed as one example of nonlinear equations possessing Lax pairs of a special form. Also this system was found as a special case of the fourreduction of the KadomtsevPetviashivilli hierarchy. We obtain exact solutions of the system by using Lie symmetry analysis along with the simplest equation and Jacobi elliptic equation methods. Also, symmetry reductions are obtained based on the optimal system of onedimensional subalgebras. In addition, the conservation laws are derived using two approaches: the new conservation theorem due to Ibragimov and the multiplier method.
http://www.boundaryvalueproblems.com/content/2014/1/248
Khadijo AdemChaudry KhaliqueBoundary Value Problems 2014, null:24820141209T12:00:00Zdoi:10.1186/s1366101402486/content/figures/s1366101402486toc.gifBoundary Value Problems16872770${item.volume}24820141209T12:00:00ZXMLGlobal nonexistence of solutions for nonlinear coupled viscoelastic wave equations with damping and source termsIn this paper, we are concerned with a nonlinear coupled viscoelastic wave equations with initialboundary value conditions and nonlinear damping and source terms. Under suitable assumptions on relaxation functions, damping terms, and source terms, by using the energy method we proved a global nonexistence result for certain solutions with negative initial energy.
http://www.boundaryvalueproblems.com/content/2014/1/250
Jianghao HaoShasha NiuHuihui MengBoundary Value Problems 2014, null:25020141128T12:00:00Zdoi:10.1186/s136610140250z/content/figures/s136610140250ztoc.gifBoundary Value Problems16872770${item.volume}25020141128T12:00:00ZXMLNew results for perturbed secondorder impulsive differential equation on the halflineBy using a variational method and some critical points theorems, we establish some results on the multiplicity of solutions for secondorder impulsive differential equation depending on two real parameters on the halfline. In addition, two examples to illustrate our results are given.
http://www.boundaryvalueproblems.com/content/2014/1/246
Yulin ZhaoXuebin WangXingguo LiuBoundary Value Problems 2014, null:24620141128T12:00:00Zdoi:10.1186/s1366101402468/content/figures/s1366101402468toc.gifBoundary Value Problems16872770${item.volume}24620141128T12:00:00ZXMLMultiplicity of solutions of perturbed Schrödinger equation with electromagnetic fields and critical nonlinearity in RNIn this paper, we deal with the existence and multiplicity of solutions for perturbed Schrödinger equation with electromagnetic fields and critical nonlinearity in
R
N
:
−
ε
2
Δ
A
u
(
x
)
+
V
(
x
)
u
(
x
)
=

u

2
∗
−
2
u
+
h
(
x
,

u

2
)
u
for all
x
∈
R
N
, where
∇
A
u
(
x
)
:
=
(
∇
+
i
A
(
x
)
)
u
,
V
(
x
)
is a nonnegative potential. By using Lions’ second concentration compactness principle and concentration compactness principle at infinity to prove that the
(
PS
)
c
condition holds locally and by variational method, we show that this equation has at least one solution provided that
ε
<
E
, for any
m
∈
N
, it has m pairs of solutions if
ε
<
E
m
, where ℰ and
E
m
are sufficiently small positive numbers.MSC:35J60, 35B33.
http://www.boundaryvalueproblems.com/content/2014/1/240
Sihua LiangYueqiang SongBoundary Value Problems 2014, null:24020141127T12:00:00Zdoi:10.1186/s1366101402401/content/figures/s1366101402401toc.gifBoundary Value Problems16872770${item.volume}24020141127T12:00:00ZXML