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The latest research articles published by Boundary Value Problems20140911T00:00:00ZTrace operator and a nonlinear boundary value problem in a new spaceWe develop a new function space and discuss trace operator on the same genealogical spaces. We also prove that the nonlinear boundary value problem with Dirichlet condition:
−
Δ
u
=
f
(

u

)
sgn
u
in the given domain,
u
=
0
on the boundary, possesses only a trivial solution if
f
obeys the slope condition:
α
′
(
x
)
>
2
n
n
−
2
α
(
x
)
x
, where
α
is the antiderivative of
f
with
α
(
0
)
=
0
.
http://www.boundaryvalueproblems.com/content/2014/1/153
Hee PakYoung ParkBoundary Value Problems 2014, null:15320140911T00:00:00Zdoi:10.1186/s136610140153z/content/figures/s136610140153ztoc.gifBoundary Value Problems16872770${item.volume}15320140911T00:00:00ZXMLStanding waves and global existence for nonlinear wave equations with potential, strong, and nonlinear damping termsThis paper is concerned with the Cauchy problem of nonlinear wave equations with potential, strong, and nonlinear damping terms. Firstly, by using variational calculus and compactness lemma, the existence of standing waves of the ground states is obtained. Then the instability of the standing wave is shown by applying potentialwell arguments and concavity methods. Finally, we show how small the initial data are for the global solutions to exist.
http://www.boundaryvalueproblems.com/content/2014/1/144
Wenyi HuangBoundary Value Problems 2014, null:14420140910T00:00:00Zdoi:10.1186/s1366101401440/content/figures/s1366101401440toc.gifBoundary Value Problems16872770${item.volume}14420140910T00:00:00ZXMLThird order problems with nonlocal conditions of integral typeWe discuss the existence of solutions of nonlinear third order ordinary differential equations with integral boundary conditions. We provide sufficient conditions on the nonlinearity and the functions appearing in the boundary conditions that guarantee the existence of at least one solution to our problem. We rely on the method of lower and upper solutions to generate an iterative technique, which is not necessarily monotone.
http://www.boundaryvalueproblems.com/content/2014/1/137
Abdelkader BoucherifSidi BouguimaZehour BenbouzianeNawal AlMalkiBoundary Value Problems 2014, null:13720140910T00:00:00Zdoi:10.1186/s136610140137z/content/figures/s136610140137ztoc.gifBoundary Value Problems16872770${item.volume}13720140910T00:00:00ZXMLExplicit solutions of wall jet flow subject to a convective boundary conditionIn this paper, an analysis is made on the laminar jet flow and heat transfer of a copperwater nanofluid over an impermeable resting wall. With the homogeneous model (Maïga et al. in Int. J. Heat Fluid Flow 26(4): 530546, 2005), the NavierStokes equations describing this heat fluid flows are reduced to a set of differential equations via similarity transformations. An implicitly analytical solution overlooked in previous publications is discovered for the velocity distribution. We further present the explicit solutions with high precision for both the velocity and the temperature distributions. A mathematical analysis shows that those explicit solutions have exponential behaviors at far field. Besides, the effects of the volumetric fraction parameter ϕ and the dimensionless heat transfer parameter γ on the velocity and temperature profiles, as well as on the reduced local skin friction coefficient and the reduced Nusselt number, are examined in detail.
http://www.boundaryvalueproblems.com/content/2014/1/163
Ammarah RaeesHang XuMuhammad RaeesulHaqBoundary Value Problems 2014, null:16320140901T09:35:12Zdoi:10.1186/168727702014163/content/figures/168727702014163toc.gifBoundary Value Problems16872770${item.volume}16320140901T09:35:12ZXMLOn exact solution of unsteady MHD flow of a viscous fluid in an orthogonal rheometerThis paper studies the unsteady MHD flow of a viscous fluid in which each point of the parallel planes are subject to the nontorsional oscillations in their own planes. The streamlines at any given time are concentric circles. Exact solutions are obtained and the loci Γ of the centres of these concentric circles are discussed. It is shown that the motion so obtained gives three infinite sets of exact solutions in the geometry of an orthogonal rheometer in which the above nontorsional oscillations are superposed on the disks. These solutions reduce to a single unique solution when symmetric solutions are looked for. Some interesting special cases are also obtained from these solutions.
http://www.boundaryvalueproblems.com/content/2014/1/146
Muhammad RanaSadia SiddiqaSaima NoorBoundary Value Problems 2014, null:14620140809T12:00:00Zdoi:10.1186/s136610140146y/content/figures/s136610140146ytoc.gifBoundary Value Problems16872770${item.volume}14620140809T12:00:00ZXMLBiharmonic equations with improved subcritical polynomial growth and subcritical exponential growthThe main purpose of this paper is to establish the existence of two nontrivial solutions and the existence of infinitely many solutions for a class of fourthorder elliptic equations with subcritical polynomial growth and subcritical exponential growth by using a suitable version of the mountain pass theorem and the symmetric mountain pass theorem.
http://www.boundaryvalueproblems.com/content/2014/1/162
Ruichang PeiJihui ZhangBoundary Value Problems 2014, null:16220140712T12:00:00Zdoi:10.1186/s136610140162y/content/figures/s136610140162ytoc.gifBoundary Value Problems16872770${item.volume}16220140712T12:00:00ZXMLInfinitely many weak solutions for a fractional Schrödinger equationIn this paper we are concerned with the fractional Schrödinger equation
(
−
Δ
)
α
u
+
V
(
x
)
u
=
f
(
x
,
u
)
,
x
∈
R
N
, where
0
<
α
<
1
,
N
>
2
α
,
(
−
Δ
)
α
stands for the fractional Laplacian of order α, V is a positive continuous potential, and f is a continuous subcritical nonlinearity. We obtain the existence of infinitely many weak solutions for the above problem by the fountain theorem in critical point theory.
http://www.boundaryvalueproblems.com/content/2014/1/159
Wei DongJiafa XuZhongli WeiBoundary Value Problems 2014, null:15920140712T12:00:00Zdoi:10.1186/s1366101401596/content/figures/s1366101401596toc.gifBoundary Value Problems16872770${item.volume}15920140712T12:00:00ZXMLThree periodic solutions for a class of ordinaryWe study the pHamiltonian systems
−
(

u
′

p
−
2
u
′
)
′
+
A
(
t
)

u

p
−
2
u
=
∇
F
(
t
,
u
)
+
λ
∇
G
(
t
,
u
)
,
u
(
0
)
−
u
(
T
)
=
u
′
(
0
)
−
u
′
(
T
)
=
0
. Three periodic solutions are obtained by using a three critical points theorem.
http://www.boundaryvalueproblems.com/content/2014/1/150
Qiong MengBoundary Value Problems 2014, null:15020140711T12:00:00Zdoi:10.1186/s1366101401502/content/figures/s1366101401502toc.gifBoundary Value Problems16872770${item.volume}15020140711T12:00:00ZXMLSimilarity method for the study of strong shock waves in magnetogasdynamicsIn this paper, a nondimensional unsteady adiabatic flow of a plane or cylindrical strong shock wave propagating in plasma is studied. The plasma is assumed to be an ideal gas with infinite electrical conductivity permeated by a transverse magnetic field. A selfsimilar solution of the problem is obtained in terms of density, velocity and pressure in the presence of magnetic field. We use the method of Lie group invariance to determine the class of selfsimilar solutions. The arbitrary constants, occurring in the expressions of the generators of the local Lie group of transformations, give rise to different cases of possible solutions with a power law, exponential or logarithmic shock paths. A particular case of the collapse of an imploding shock is worked out in detail. Numerical calculations have been performed to obtain the similarity exponents and the profiles of flow variables. Our results are found in good agreement with the known results. All computational work is performed by using software package MATHEMATICA.
http://www.boundaryvalueproblems.com/content/2014/1/142
Rajan AroraSanjay YadavMohd SiddiquiBoundary Value Problems 2014, null:14220140711T12:00:00Zdoi:10.1186/s1366101401422/content/figures/s1366101401422toc.gifBoundary Value Problems16872770${item.volume}14220140711T12:00:00ZXMLLinear overdetermined boundary value problems in Hilbert spaceThe general linear boundary value problem for an abstract functional differential equation is considered in the case that the number of boundary conditions is greater than the dimension of the nullspace to the corresponding homogeneous equation. Sufficient conditions of the solvability of the problem are obtained. A case of a functional differential system with aftereffect is considered separately.
http://www.boundaryvalueproblems.com/content/2014/1/140
Vladimir MaksimovBoundary Value Problems 2014, null:14020140711T12:00:00Zdoi:10.1186/s1366101401404/content/figures/s1366101401404toc.gifBoundary Value Problems16872770${item.volume}14020140711T12:00:00ZXML