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The latest research articles published by Boundary Value Problems20141122T12:00:00ZSolvability of n thorder Lipschitz equations with nonlinear threepoint boundary conditionsIn this paper, we investigate the solvability of nthorder Lipschitz equations
y
(
n
)
=
f
(
x
,
y
,
y
′
,
…
,
y
(
n
−
1
)
)
,
x
1
≤
x
≤
x
3
, with nonlinear threepoint boundary conditions of the form
k
(
y
(
x
2
)
,
y
′
(
x
2
)
,
…
,
y
(
n
−
1
)
(
x
2
)
;
y
(
x
1
)
,
y
′
(
x
1
)
,
…
,
y
(
n
−
1
)
(
x
1
)
)
=
0
,
g
i
(
y
(
i
)
(
x
2
)
,
y
(
i
+
1
)
(
x
2
)
,
…
,
y
(
n
−
1
)
(
x
2
)
)
=
0
,
i
=
0
,
1
,
…
,
n
−
3
,
h
(
y
(
x
2
)
,
y
′
(
x
2
)
,
…
,
y
(
n
−
1
)
(
x
2
)
;
y
(
x
3
)
,
y
′
(
x
3
)
,
…
,
y
(
n
−
1
)
(
x
3
)
)
=
0
, where
n
≥
3
,
x
1
<
x
2
<
x
3
. By using the matching technique together with setvalued function theory, the existence and uniqueness of solutions for the problems are obtained. Meanwhile, as an application of our results, an example is given.MSC:34B10, 34B15.
http://www.boundaryvalueproblems.com/content/2014/1/239
Minghe PeiSung ChangBoundary Value Problems 2014, null:23920141122T12:00:00Zdoi:10.1186/s1366101402397/content/figures/s1366101402397toc.gifBoundary Value Problems16872770${item.volume}23920141122T12:00:00ZXMLAsymptotically linear systems near and at resonanceThis paper deals with an elliptic system of the form
−
Δ
u
=
λ
θ
1
a
(
x
)
v
+
f
(
λ
,
x
,
v
)
in Ω,
−
Δ
v
=
λ
θ
2
a
(
x
)
u
+
g
(
λ
,
x
,
u
)
in Ω,
u
=
0
=
v
on ∂Ω, where
λ
∈
R
is a parameter and
Ω
⊂
R
N
(
N
≥
1
) is a bounded domain with
C
2
,
ξ
boundary ∂Ω,
ξ
∈
(
0
,
1
)
(a bounded open interval if
N
=
1
). Here
a
(
x
)
∈
L
∞
(
Ω
)
with
a
(
x
)
>
0
a.e. in Ω and
θ
1
,
θ
2
>
0
are constants. The nonlinear perturbations
f
,
g
:
R
×
Ω
×
R
→
R
are Carathéodory functions that are sublinear at infinity. We provide sufficient conditions for determining the λdirection to which a continuum of positive and negative solutions emanates from infinity at the first eigenvalue of the associated linear problem. Furthermore, as a consequence of main results, we also provide sufficient condition for the solvability of a class of asymptotically linear system near and at resonance satisfying LandesmanLazer type conditions.MSC:35J60.
http://www.boundaryvalueproblems.com/content/2014/1/242
Maya ChhetriPetr GirgBoundary Value Problems 2014, null:24220141120T00:00:00Zdoi:10.1186/s136610140242z/content/figures/s136610140242ztoc.gifBoundary Value Problems16872770${item.volume}24220141120T00:00:00ZXMLSolutions of biharmonic equations with mixed nonlinearityIn this paper, we study the following biharmonic equations with mixed nonlinearity:
Δ
2
u
−
Δ
u
+
V
(
x
)
u
=
f
(
x
,
u
)
+
λ
ξ
(
x
)

u

p
−
2
u
,
x
∈
R
N
,
u
∈
H
2
(
R
N
)
, where
V
∈
C
(
R
N
)
,
ξ
∈
L
2
2
−
p
(
R
N
)
,
1
≤
p
<
2
, and
λ
>
0
is a parameter. The existence of multiple solutions is obtained via variational methods. Some recent results are improved and extended.MSC:35J35, 35J60.
http://www.boundaryvalueproblems.com/content/2014/1/238
Bin LiuBoundary Value Problems 2014, null:23820141108T12:00:00Zdoi:10.1186/s1366101402388/content/figures/s1366101402388toc.gifBoundary Value Problems16872770${item.volume}23820141108T12:00:00ZXMLSampling theorems for SturmLiouville problem with moving discontinuity pointsIn this paper, we investigate the sampling analysis for a new SturmLiouville problem with symmetrically located discontinuities which are defined depending on a parameter in a neighborhood of a midpoint of the interval. Also the problem has transmission conditions at these points of discontinuity and includes an eigenparameter in a boundary condition. We establish briefly the relations needed for the derivations of the sampling theorems and construct the Green’s function for the problem. Then we derive sampling representations for the solutions and Green’s functions.MSC:34B24, 34B27, 94A20.
http://www.boundaryvalueproblems.com/content/2014/1/237
Fatma H¿raNihat Alt¿n¿¿¿kBoundary Value Problems 2014, null:23720141108T12:00:00Zdoi:10.1186/s1366101402379/content/figures/s1366101402379toc.gifBoundary Value Problems16872770${item.volume}23720141108T12:00:00ZXMLAn approach to the numerical verification of solutions for variational inequalities using Schauder fixed point theoryIn this paper, we describe a numerical method to verify the existence of solutions for a unilateral boundary value problems for second order equation governed by the variational inequalities. It is based on Nakao’s method by using finite element approximation and its explicit error estimates for the problem. Using the Riesz representation theory in Hilbert space, we first transform the iterative procedure of variational inequalities into a fixed point form. Then, using Schauder fixed point theory, we construct a high efficiency numerical verification method that through numerical computation generates a bounded, closed, convex set which includes the approximate solution. Finally, a numerical example is illustrated.MSC:65G20, 65G30, 65N15, 65N30.
http://www.boundaryvalueproblems.com/content/2014/1/235
Cheon RyooBoundary Value Problems 2014, null:23520141107T12:00:00Zdoi:10.1186/s136610140235y/content/figures/s136610140235ytoc.gifBoundary Value Problems16872770${item.volume}23520141107T12:00:00ZXMLPeriodic solution of secondorder impulsive delay differential system via generalized mountain pass theoremIn this paper we use variational methods and generalized mountain pass theorem to investigate the existence of periodic solutions for some secondorder delay differential systems with impulsive effects. To the authors’ knowledge, there is no paper about periodic solution of impulses delay differential systems via critical point theory. Our results are completely new.
http://www.boundaryvalueproblems.com/content/2014/1/234
Dechu ChenBinxiang DaiBoundary Value Problems 2014, null:23420141106T12:00:00Zdoi:10.1186/s136610140234z/content/figures/s136610140234ztoc.gifBoundary Value Problems16872770${item.volume}23420141106T12:00:00ZXMLUniqueness results for the Dirichlet problem for higher order elliptic equations in polyhedral anglesWe consider the Dirichlet boundary value problem for higher order elliptic equations in divergence form with discontinuous coefficients in polyhedral angles. Some uniqueness results are proved.MSC:35J30, 35J40.
http://www.boundaryvalueproblems.com/content/2014/1/232
Sara MonsurròIlia TavkhelidzeMaria TransiricoBoundary Value Problems 2014, null:23220141104T12:00:00Zdoi:10.1186/s1366101402321/content/figures/s1366101402321toc.gifBoundary Value Problems16872770${item.volume}23220141104T12:00:00ZXMLLazerLeach type condition for second order differential equations at resonance with impulsive effects via variational methodIn this paper, we study the existence of periodic solutions of second order impulsive differential equations at resonance with impulsive effects. We prove the existence of periodic solutions under a generalized LazerLeach type condition by using variational method. The impulses can generate a periodic solution.
http://www.boundaryvalueproblems.com/content/2014/1/233
Jin LiBoundary Value Problems 2014, null:23320141031T12:00:00Zdoi:10.1186/s1366101402330/content/figures/s1366101402330toc.gifBoundary Value Problems16872770${item.volume}23320141031T12:00:00ZXMLOn global solution, energy decay and blowup for 2D Kirchhoff equation with exponential termsThis paper is concerned with the study of damped wave equation of Kirchhoff type
u
t
t
−
M
(
∥
∇
u
(
t
)
∥
2
2
)
△
u
+
u
t
=
g
(
u
)
in
Ω
×
(
0
,
∞
)
, with initial and Dirichlet boundary condition, where Ω is a bounded domain of
R
2
having a smooth boundary ∂Ω. Under the assumption that g is a function with exponential growth at infinity, we prove global existence and the decay property as well as blowup of solutions in finite time under suitable conditions.MSC:35L70, 35B40, 35B44.
http://www.boundaryvalueproblems.com/content/2014/1/230
Gongwei LiuBoundary Value Problems 2014, null:23020141023T12:00:00Zdoi:10.1186/s1366101402303/content/figures/s1366101402303toc.gifBoundary Value Problems16872770${item.volume}23020141023T12:00:00ZXMLPeriodic oscillation in suspension bridge model with a periodic damping termWe study periodic solutions of the suspension bridge model proposed by Lazer and McKenna with a periodic damping term. Under the Dolphtype condition and a small periodic damping term condition, the existence and the uniqueness of a periodic solution have been proved by a constructive method. Two numerical examples are presented to illustrate the effect of the periodic damping term.MSC:34B15, 34C15, 34C25.
http://www.boundaryvalueproblems.com/content/2014/1/231
Lin WangJian ZuBoundary Value Problems 2014, null:23120141016T12:00:00Zdoi:10.1186/s1366101402312/content/figures/s1366101402312toc.gifBoundary Value Problems16872770${item.volume}23120141016T12:00:00ZXML