Boundary Value Problems  Latest Articles
http://www.boundaryvalueproblems.com
The latest research articles published by Boundary Value Problems20140809T12:00:00ZOn 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${item.volume}14020140711T12:00:00ZXMLThe effect of initial stress and magnetic field on wave propagation in human dry bonesThe aim of the present paper is to study the influence of initial stress and magnetic field on the propagation of harmonic waves in a human long dry bone as transversely isotropic material, subject to the boundary conditions that the outer and inner surfaces are traction free. The equations of elastodynamics are solved in terms of displacements. The natural frequency of plane vibrations in the case of harmonic vibrations has been obtained. The frequencies and phase velocity are calculated numerically, the effects of initial stress and magnetic field are discussed. Comparisons are made with the result in the absence of initial stress and magnetic field.MSC:
74B05.
http://www.boundaryvalueproblems.com/content/2014/1/135
Samy MahmoudAbdelouahed TounsiAhmed AliKhalil AlBasyouniBoundary Value Problems 2014, null:13520140527T15:46:29Zdoi:10.1186/168727702014135/content/figures/168727702014135toc.gifBoundary Value Problems16872770${item.volume}13520140527T15:46:29ZXMLAnalysis of the inverse problem in a time fractional parabolic equation with mixed boundary conditionsThis article deals with the mathematical analysis of the inverse coefficient problem of identifying the unknown coefficient k(x) in the linear time fractional parabolic equation Dtαu(x,t)=(k(x)ux)x, 0<α≤1, with mixed boundary conditions u(0,t)=ψ0(t), ux(1,t)=ψ1(t). By defining the inputoutput mappings Φ[⋅]:K→C1[0,T] and Ψ[⋅]:K→C[0,T], the inverse problem is reduced to the problem of their invertibility. Hence the main purpose of this study is to investigate the distinguishability of the inputoutput mappings Φ[⋅] and Ψ[⋅]. This work shows that the inputoutput mappings Φ[⋅] and Ψ[⋅] have the distinguishability property. Moreover, the value k(0) of the unknown diffusion coefficient k(x) at x=0 can be determined explicitly by making use of measured output data (boundary observation) k(0)ux(0,t)=f(t), which brings greater restriction on the set of admissible coefficients. It is also shown that the measured output data f(t) and h(t) can be determined analytically by a series representation, which implies that the inputoutput mappings Φ[⋅]:K→C1[0,T] and Ψ[⋅]:K→C[0,T] can be described explicitly.
http://www.boundaryvalueproblems.com/content/2014/1/134
Ebru OzbilgeAli DemirBoundary Value Problems 2014, null:13420140527T14:51:32Zdoi:10.1186/168727702014134/content/figures/168727702014134toc.gifBoundary Value Problems16872770${item.volume}13420140527T14:51:32ZXMLA remark on the aminimally thin sets associated with the Schrödinger operatorThe aim of this paper is to give a new criterion for aminimally thin sets at infinity with respect to the Schrödinger operator in a cone, which supplement the results obtained by T. Zhao.
http://www.boundaryvalueproblems.com/content/2014/1/133
Gaixian XueBoundary Value Problems 2014, null:13320140523T11:15:55Zdoi:10.1186/168727702014133/content/figures/168727702014133toc.gifBoundary Value Problems16872770${item.volume}13320140523T11:15:55ZXMLSignchanging solution for a thirdorder boundaryvalue problem in ordered Banach space with lattice structureIn this paper, the signchanging solution of a thirdorder twopoint boundaryvalue problem is considered. By calculating the eigenvalues and the algebraic multiplicity of the linear problem and using a new fixed point theorem in an ordered Banach space with lattice structure, we give some conditions to guarantee the existence for a signchanging solution.
http://www.boundaryvalueproblems.com/content/2014/1/132
Xiuli LinZengqin ZhaoBoundary Value Problems 2014, null:13220140522T17:50:26Zdoi:10.1186/168727702014132/content/figures/168727702014132toc.gifBoundary Value Problems16872770${item.volume}13220140522T17:50:26ZXML