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The latest research articles published by Boundary Value Problems20151125T12:00:00Z On the global existence of 3D magnetohydrodynamic system in the critical spaces In this article, we prove the global existence of the threedimensional inhomogeneous incompressible magnetohydrodynamic system under the assumptions that the initial velocity field and the initial conductivity are small in the critical space
B
˙
2
,
1
1
/
2
(
R
3
)
.MSC: 35Q35, 76D03.
http://www.boundaryvalueproblems.com/content/2015/1/218
Xiaolian AiZilai LiBoundary Value Problems 2015, null:21820151125T12:00:00Zdoi:10.1186/s1366101504728/content/figures/s1366101504728toc.gifBoundary Value Problems16872770${item.volume}21820151125T12:00:00ZXML Boundary value problems for modified Helmholtz equations and applications We investigate factorizations of modified Helmholtz equations in Clifford algebra
C
l
(
V
3
,
3
)
. Using the method of fundamental solutions for modified Helmholtz equations and Clifford calculus, we obtain some integral representation theorem in Clifford analysis. The boundedness of singular integral operators in Hölder space is given. Moreover, we establish solvability conditions of Riemann type problems for modified Helmholtz equations in Clifford analysis. As applications, we solve a kind of singular integral equations. The explicit representation of the solution is also given.MSC: 30G35.
http://www.boundaryvalueproblems.com/content/2015/1/217
Longfei GuZunwei FuBoundary Value Problems 2015, null:21720151125T12:00:00Zdoi:10.1186/s1366101504871/content/figures/s1366101504871toc.gifBoundary Value Problems16872770${item.volume}21720151125T12:00:00ZXML The exact asymptotic behavior of blowup solutions to a highly degenerate elliptic problem In this paper, by constructing new comparison functions, we mainly study the boundary behavior of solutions to boundary blowup elliptic problems for more general nonlinearities f (which may be rapidly varying at infinity)
△
∞
u
=
b
(
x
)
f
(
u
)
,
x
∈
Ω
,
u

∂
Ω
=
+
∞
, where Ω is a bounded domain with smooth boundary in
R
N
, and
b
∈
C
(
Ω
¯
)
which is positive in Ω and may be vanishing on the boundary and rapidly varying near the boundary.
http://www.boundaryvalueproblems.com/content/2015/1/216
Ling MiBoundary Value Problems 2015, null:21620151125T00:00:00Zdoi:10.1186/s1366101504826/content/figures/s1366101504826toc.gifBoundary Value Problems16872770${item.volume}21620151125T00:00:00ZXML Existence of solutions for a class of quasilinear Schrödinger equations on <inlineformula> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" name="s1366101504862i1"> <m:mi mathvariant="doublestruck">R</m:mi> </m:math> </inlineformula> In this paper, we study the existence of nontrivial solution for a class of quasilinear Schrödinger equations in
R
with the nonlinearity asymptotically linear and, furthermore, the potential indefinite in sign. The tool used in this paper is the direct variation method.MSC: 34J10, 35J20, 35J60.
http://www.boundaryvalueproblems.com/content/2015/1/215
DaBin WangKuo YangBoundary Value Problems 2015, null:21520151125T00:00:00Zdoi:10.1186/s1366101504862/content/figures/s1366101504862toc.gifBoundary Value Problems16872770${item.volume}21520151125T00:00:00ZXML Positive solutions for higher order differential equations with integral boundary conditions In this paper, we consider the existence of at least three positive solutions for the 2nth order differential equations with integral boundary conditions{
x
(
2
n
)
(
t
)
=
f
(
t
,
x
(
t
)
,
x
″
(
t
)
,
…
,
x
(
2
(
n
−
1
)
)
(
t
)
)
,
0
≤
t
≤
1
,
x
(
2
i
)
(
0
)
=
∫
0
1
k
i
(
s
)
x
(
2
i
)
(
s
)
d
s
,
x
(
2
i
)
(
1
)
=
0
,
0
≤
i
≤
n
−
1
,where
(
−
1
)
n
f
>
0
is continuous, and
k
i
(
t
)
∈
L
1
[
0
,
1
]
(
i
=
0
,
1
,
…
,
n
−
1
) are nonnegative. The associated Green’s function for the higher order differential equations with integral boundary conditions is first given, and growth conditions are imposed on f which yield the existence of multiple positive solutions by using the LeggettWilliams fixed point theorem.
http://www.boundaryvalueproblems.com/content/2015/1/214
Yude JiYanping GuoYukun YaoBoundary Value Problems 2015, null:21420151125T00:00:00Zdoi:10.1186/s1366101504853/content/figures/s1366101504853toc.gifBoundary Value Problems16872770${item.volume}21420151125T00:00:00ZXML Nonsimultaneous blowup of a reactiondiffusion system with inner absorption and coupled via nonlinear boundary flux This paper deals with a parabolic reactiondiffusion system with a nonlinear absorption term, meanwhile the two equations of the system coupled via nonlinear boundary flux which obey different laws. Under the hypothesis condition of the initial data, we get the sufficient and necessary conditions under which there exist initial data such that nonsimultaneous blowup occurs.MSC: 35B33, 35K65, 35K55.
http://www.boundaryvalueproblems.com/content/2015/1/213
Si XuBoundary Value Problems 2015, null:21320151121T00:00:00Zdoi:10.1186/s1366101504835/content/figures/s1366101504835toc.gifBoundary Value Problems16872770${item.volume}21320151121T00:00:00ZXML Existence and <it>n</it>multiplicity of positive periodic solutions for impulsive functional differential equations with two parameters In this paper, we employ the wellknown Krasnoselskii fixed point theorem to study the existence and nmultiplicity of positive periodic solutions for the periodic impulsive functional differential equations with two parameters. The form including an impulsive term of the equations in this paper is rather general and incorporates as special cases various problems which have been studied extensively in the literature. Easily verifiable sufficient criteria are obtained for the existence and nmultiplicity of positive periodic solutions of the impulsive functional differential equations.MSC: 34K20.
http://www.boundaryvalueproblems.com/content/2015/1/212
Qiong MengJurang YanBoundary Value Problems 2015, null:21220151118T12:00:00Zdoi:10.1186/s1366101504782/content/figures/s1366101504782toc.gifBoundary Value Problems16872770${item.volume}21220151118T12:00:00ZXML On the twopoint problem for implicit secondorder ordinary differential equations Given a nonempty set
Y
⊆
R
n
and a function
f
:
[
a
,
b
]
×
R
n
×
R
n
×
Y
→
R
, we are interested in the problem of finding
u
∈
W
2
,
p
(
[
a
,
b
]
,
R
n
)
such that{
f
(
t
,
u
(
t
)
,
u
′
(
t
)
,
u
″
(
t
)
)
=
0
for a.e.
t
∈
[
a
,
b
]
,
u
(
a
)
=
u
(
b
)
=
0
R
n
.We prove an existence result where, for any fixed
(
t
,
y
)
∈
[
a
,
b
]
×
Y
, the function
f
(
t
,
⋅
,
⋅
,
y
)
can be discontinuous even at all points
(
x
,
z
)
∈
R
n
×
R
n
. The function
f
(
t
,
x
,
z
,
⋅
)
is only assumed to be continuous and locally nonconstant.We also show how the same approach can be applied to the implicit integral equation
f
(
t
,
∫
a
b
g
(
t
,
z
)
u
(
z
)
d
z
,
u
(
t
)
)
=
0
. We prove an existence result (with
f
(
t
,
x
,
y
)
discontinuous in x and continuous and locally nonconstant in y) which extends and improves in several directions some recent results in the field.
http://www.boundaryvalueproblems.com/content/2015/1/211
Paolo CubiottiJenChih YaoBoundary Value Problems 2015, null:21120151117T12:00:00Zdoi:10.1186/s1366101504755/content/figures/s1366101504755toc.gifBoundary Value Problems16872770${item.volume}21120151117T12:00:00ZXML Largetime behavior of the strong solution to nonhomogeneous incompressible MHD system with general initial data This paper investigates the largetime behavior of strong solutions to the nonhomogeneous incompressible magnetohydrodynamic equations on a bounded domain in
R
2
. Based on uniform estimates, we prove that the velocity, the magnetic field, and their derivatives converge to zero in
L
2
norm as time goes to infinity without any additional assumption on the initial data and external force by a pure energy method.MSC: 76W05, 76N10, 35B40, 35B45.
http://www.boundaryvalueproblems.com/content/2015/1/210
Shengquan LiuBoundary Value Problems 2015, null:21020151117T12:00:00Zdoi:10.1186/s1366101504719/content/figures/s1366101504719toc.gifBoundary Value Problems16872770${item.volume}21020151117T12:00:00ZXML Nonuniformly asymptotically linear fourthorder elliptic problems The existence of multiple solutions for a class of fourthorder elliptic equations with respect to the nonuniformly asymptotically linear conditions is established by using the minimax method and Morse theory.
http://www.boundaryvalueproblems.com/content/2015/1/209
Ruichang PeiJihui ZhangBoundary Value Problems 2015, null:20920151114T12:00:00Zdoi:10.1186/s1366101504737/content/figures/s1366101504737toc.gifBoundary Value Problems16872770${item.volume}20920151114T12:00:00ZXML