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The latest research articles published by Boundary Value Problems20150227T12:00:00ZMultiple solutions for the p Laplacian problem with supercritical exponentIn this paper, we explore the existence of multiple solutions to the following pLaplacian type of equation with supercritical Sobolevexponent:{
−
Δ
p
u
+

u

r
−
2
u
=
γ

u

s
−
2
u
in
Ω
,
u
=
0
on
∂
Ω
,where Ω is a smoothly bounded open domain in
R
n
(
n
>
p
⩾
2
),
r
>
p
∗
,
p
∗
≜
n
p
n
−
p
is a critical Sobolev exponent. We prove that if
1
<
s
<
p
<
n
and
γ
∈
R
+
, the above equation possesses infinitely many weak solutions. Furthermore, if
1
<
s
=
p
<
n
and
λ
m
<
γ
⩽
λ
m
+
1
, there exists at least mpair nontrivial solutions, where
λ
m
is the meigenvalue value defined in (2.2).
http://www.boundaryvalueproblems.com/content/2015/1/44
Yansheng ZhongBoundary Value Problems 2015, null:4420150227T12:00:00Zdoi:10.1186/s136610150304x/content/figures/s136610150304xtoc.gifBoundary Value Problems16872770${item.volume}4420150227T12:00:00ZXMLBlow up of positive initialenergy solutions for coupled nonlinear wave equations with degenerate damping and source termsIn this work, we consider coupled nonlinear wave equations with degenerate damping and source terms. We will show the blow up of solutions in finite time with positive initial energy. This improves earlier results in the literature.MSC: 35B44, 35L05.
http://www.boundaryvalueproblems.com/content/2015/1/43
Erhan Pi¿kinBoundary Value Problems 2015, null:4320150227T00:00:00Zdoi:10.1186/s1366101503068/content/figures/s1366101503068toc.gifBoundary Value Problems16872770${item.volume}4320150227T00:00:00ZXMLExistence of unbounded solutions of boundary value problems for singular differential systems on whole lineMotivated by (Kyoung and YongHoon in Sci. China Math. 53:967984, 2010) and (Chen and Zhang in Sci. China Math. 54:959972, 2011), this paper is concerned with a boundary value problem of singular secondorder differential systems with quasiLaplacian operators on the whole line. By constructing a completely continuous nonlinear operator and using a fixed point theorem, sufficient conditions guaranteeing the existence of at least one unbounded solution are established. The methods used are standard, however, their exposition in the framework of such a kind of problems is new and skillful. Three concrete examples are given to illustrate the main theorem.MSC: 34B10, 34B15, 35B10.
http://www.boundaryvalueproblems.com/content/2015/1/42
Xiaohui YangYuji LiuBoundary Value Problems 2015, null:4220150225T00:00:00Zdoi:10.1186/s1366101503001/content/figures/s1366101503001toc.gifBoundary Value Problems16872770${item.volume}4220150225T00:00:00ZXMLAn operator method for telegraph partial differential and difference equationsThe Cauchy problem for abstract telegraph equations
d
2
u
(
t
)
d
t
2
+
α
d
u
(
t
)
d
t
+
A
u
(
t
)
+
β
u
(
t
)
=
f
(
t
)
(
0
≤
t
≤
T
),
u
(
0
)
=
φ
,
u
′
(
0
)
=
ψ
in a Hilbert space H with the selfadjoint positive definite operator A is studied. Stability estimates for the solution of this problem are established. The first and second order of accuracy difference schemes for the approximate solution of this problem are presented. Stability estimates for the solution of these difference schemes are established. In applications, two mixed problems for telegraph partial differential equations are investigated. The methods are illustrated by numerical examples.
http://www.boundaryvalueproblems.com/content/2015/1/41
Allaberen AshyralyevMahmut ModanliBoundary Value Problems 2015, null:4120150224T12:00:00Zdoi:10.1186/s136610150302z/content/figures/s136610150302ztoc.gifBoundary Value Problems16872770${item.volume}4120150224T12:00:00ZXMLOne class of generalized boundary value problem for analytic functionsIn this paper, a boundary value problem for analytic functions with two unknown functions on two parallel straight lines is studied, the general solutions in the different domains as well as the conditions of solvability are obtained in class
{
1
}
, and the behaviors of solutions are discussed at
z
=
∞
and in the different domains, respectively. Therefore, the classic Riemann boundary value problem is extended further.
http://www.boundaryvalueproblems.com/content/2015/1/40
Pingrun LiBoundary Value Problems 2015, null:4020150224T12:00:00Zdoi:10.1186/s1366101503010/content/figures/s1366101503010toc.gifBoundary Value Problems16872770${item.volume}4020150224T12:00:00ZXMLThe existence of solutions for impulsive p Laplacian boundary value problems at resonance on the halflineBy using the continuous theorem of Ge and Ren and constructing suitable Banach spaces and operators, we investigate the existence of solutions for an impulsive pLaplacian boundary value problem with integral boundary condition at resonance on the halfline. An example is given to illustrate our main results.MSC: 34B40.
http://www.boundaryvalueproblems.com/content/2015/1/39
Weihua JiangBoundary Value Problems 2015, null:3920150224T12:00:00Zdoi:10.1186/s1366101502993/content/figures/s1366101502993toc.gifBoundary Value Problems16872770${item.volume}3920150224T12:00:00ZXMLWellposedness of a parabolic equation with nonlocal boundary conditionIn the present study, the problem of a parabolic equation with nonlocal condition is investigated. The positivity of the second order differential operator
A
x
defined by the formulaA
x
u
(
x
)
=
−
u
″
(
x
)
+
σ
u
(
x
)
,
x
∈
(
0
,
l
)with the domainD
(
A
x
)
=
{
u
:
u
,
u
″
∈
C
[
0
,
l
]
,
u
(
0
)
=
0
,
u
′
(
0
)
=
u
′
(
l
)
+
β
u
(
l
)
}is established in the Banach space
C
[
0
,
l
]
of all continuous functions
ϕ
(
x
)
defined on
[
0
,
l
]
with the norm∥
ϕ
∥
C
[
0
,
l
]
=
max
0
≤
x
≤
l

ϕ
(
x
)

.The wellposedness of this problem in Hölder spaces in t is proved.
http://www.boundaryvalueproblems.com/content/2015/1/38
Allaberen AshyralyevAbdizhahan SarsenbiBoundary Value Problems 2015, null:3820150224T12:00:00Zdoi:10.1186/s1366101502975/content/figures/s1366101502975toc.gifBoundary Value Problems16872770${item.volume}3820150224T12:00:00ZXMLSymmetric solutions for singular quasilinear elliptic systems involving multiple critical HardySobolev exponentsThis paper deals with the existence and multiplicity of symmetric solutions for a class of singular quasilinear elliptic systems involving multiple critical HardySobolev exponents in a bounded symmetric domain. Based upon the symmetric criticality principle of Palais and variational methods, we establish several existence and multiplicity results of Gsymmetric solutions under certain appropriate hypotheses on the weighted functions and the parameters.MSC: 35J25, 35J60, 35J65.
http://www.boundaryvalueproblems.com/content/2015/1/37
Zhiying DengYisheng HuangBoundary Value Problems 2015, null:3720150224T12:00:00Zdoi:10.1186/s1366101502966/content/figures/s1366101502966toc.gifBoundary Value Problems16872770${item.volume}3720150224T12:00:00ZXMLPeriodic solutions of a class of nonautonomous secondorder Hamiltonian systems with nonsmooth potentialsThis paper is concerned with nonautonomous secondorder Hamiltonian systems with nondifferentiable potentials. By using the nonsmooth critical point theory for locally Lipschitz functionals, we obtain some new existence results for the periodic solutions.
http://www.boundaryvalueproblems.com/content/2015/1/34
Yan NingTianqing AnBoundary Value Problems 2015, null:3420150220T12:00:00Zdoi:10.1186/s136610150292x/content/figures/s136610150292xtoc.gifBoundary Value Problems16872770${item.volume}3420150220T12:00:00ZXMLSampling of vectorvalued transforms associated with solutions and Green¿s matrix of discontinuous Dirac systemsOur goal in the current paper is to derive the sampling theorems of a Dirac system with a spectral parameter appearing linearly in the boundary conditions and also with an internal point of discontinuity. To derive the sampling theorems including the construction of Green’s matrix as well as the eigenvectorfunction expansion theorem, we briefly study the spectral analysis of the problem as in Levitan and Sargsjan (Translations of Mathematical Monographs, vol. 39, 1975; SturmLiouville and Dirac Operators, 1991) in a way similar to that of Fulton (Proc. R. Soc. Edinb. A 77:293308, 1977) and Kerimov (Differ. Equ. 38(2):164174, 2002). We derive sampling representations for transforms whose kernels are either solutions or Green’s matrix of the problem. In the special case, when our problem is continuous, the obtained results coincide with the corresponding results in Annaby and Tharwat (J. Appl. Math. Comput. 36:291317, 2011).MSC: 34L16, 94A20, 65L15.
http://www.boundaryvalueproblems.com/content/2015/1/33
Mohammed TharwatAbdulaziz AlofiBoundary Value Problems 2015, null:3320150220T12:00:00Zdoi:10.1186/s136610150290z/content/figures/s136610150290ztoc.gifBoundary Value Problems16872770${item.volume}3320150220T12:00:00ZXML