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Korean Journal of Mathematics
Journal Basic Information
pISSN :
19768605
eISSN :
22881433
Journal DOI :
10.11568/kjm
Frequency :
Others
Publisher:
The KangwonKyungki Mathematical Society
Editor in Chief :
GiSang Cheon
Volume & Issues
Volume 16, Issue 4  Dec 2008
Volume 16, Issue 3  Sep 2008
Volume 16, Issue 2  Jun 2008
Volume 16, Issue 1  Mar 2008
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1
EXISTENCE OF SIX SOLUTIONS OF THE NONLINEAR SUSPENSION BRIDGE EQUATION WITH NONLINEARITY CROSSING THREE IGENVALUES
Jung, TackSun ; Choi, Q.Heung ;
Korean Journal of Mathematics, volume 16, issue 1, 2008, Pages 1~24
Abstract
Let Lu =
+
and E be the complete normed space spanned by the eigenfunctions of L. We reveal the existence of six nontrivial solutions of a nonlinear suspension bridge equation Lu +
= 1 +
in E when the nonlinearity crosses three eigenvalues. It is shown by the critical point theory induced from the limit relative category of the torus with three holes and finite dimensional reduction method.
2
A SHAPE OPTIMIZATION METHOD USING COMPLIANT FORMULATION ASSOCIATED WITH THE 2D STOKES CHANNEL FLOWS
Kim, HongChul ;
Korean Journal of Mathematics, volume 16, issue 1, 2008, Pages 25~40
Abstract
We are concerned with a free boundary problem for the 2D Stokes channel flows, which determines the profile of the wing for the channel, so that the given traction force is to be distributed along the wing of the channel. Using the domain embedding technique, the free boundary problem is transferred into the shape optimization problem through the compliant formulation by releasing the traction condition along the variable boundary. The justification of the formulation will be discussed.
3
NEGATIVE SOLUTION FOR THE SYSTEM OF THE NONLINEAR WAVE EQUATIONS WITH CRITICAL GROWTH
Jung, TackSun ; Choi, QHeung ;
Korean Journal of Mathematics, volume 16, issue 1, 2008, Pages 41~49
Abstract
We show the existence of a negative solution for the system of the following nonlinear wave equations with critical growth, under Dirichlet boundary condition and periodic condition

=
+
+
+
+ f,

=
+
+
+ g, where
,
> 1 are real constants,
= max{u,0}, s, t
R,
is the eigenfunction corresponding to the positive eigenvalue
of the wave operator and f, g are
, even in x and t and bounded functions.
4
REPULSIVE FIXEDPOINTS OF THE LAGUERRELIKE ITERATION FUNCTIONS
Ham, YoonMee ; Lee, SangGu ;
Korean Journal of Mathematics, volume 16, issue 1, 2008, Pages 51~55
Abstract
Let f be an analytic function with a simple zero in the reals or the complex numbers. An extraneous fixedpoint of an iteration function is a fixedpoint different from a zero of f. We prove that all extraneous fixedpoints of Laguerrelike iteration functions and general Laguerrelike functions are repulsive.
5
A BOUNDARY CONTROL PROBLEM FOR THE TIMEDEPENDENT 2D NAVIERSTOKES EQUATIONS
Kim, HongChul ; Kim, SeonGyu ;
Korean Journal of Mathematics, volume 16, issue 1, 2008, Pages 57~84
Abstract
In this paper, a boundary control problem for a flow governed by the timedependent two dimensional NavierStokes equations is considered. We derive a mathematical formulation and a relevant process for an appropriate control along the part of the boundary to minimize the drag due to the flow. After showing the existence of an optimal solution, the first order optimality conditions are derived. The strict differentiability of the state solution in regard to the control parameter shall be exposed rig orously, and the necessary conditions along with the system for the optimal solution shall be deduced in conjunction with the evaluation of the first order Gateaux derivative to the performance functional.
6
A FOURIER MULTIPLIER THEOREM ON THE BESOVLIPSCHITZ SPACES
Cho, YongKum ; Kim, DoHie ;
Korean Journal of Mathematics, volume 16, issue 1, 2008, Pages 85~90
Abstract
We consider Fourier multiplier operators whose sym bols satisfy a generalization of H
ormander's condition and establish their Sobolevtype mapping properties on the homogeneous Besov Lipschitz spaces by making use of a continuous characterization of BesovLipschitz spaces. As an application, we derive Sobolevtype imbedding theorem.
7
NONLINEAR DIFFERENTIAL EQUATIONS OF SECOND ORDER IN A HILBERT SPACE
Kim, RakJoong ;
Korean Journal of Mathematics, volume 16, issue 1, 2008, Pages 91~101
Abstract
Let H be a Hilbert space. Assume that 0
and r(t) > 0 in I = [0 T]. By means of the fixed point theorem of LeraySchauder type the existence principles of solutions for two point boundary value problems of the form (r(t)x'(t))' + f(t,x(t),r(t)x'(t)) = 0, t
I x(0) = x(T) = 0 are established where f satisfies for positive constants a, b and c
+ c for all (t,x,y)
I
H
H.
8
THE STABILITY OF PEXIDERIZED COSINE FUNCTIONAL EQUATIONS
Kim, GwangHui ;
Korean Journal of Mathematics, volume 16, issue 1, 2008, Pages 103~114
Abstract
In this paper, we investigate the superstability problem for the pexiderized cosine functional equations f(x+y)+f(xy) = 2g(x)h(y), f(x + y) + g(x  y) = 2f(x)g(y), f(x + y) + g(x  y) = 2g(x)f(y). Consequently, we have generalized the results of stability for the cosine(d'Alembert) and the Wilson functional equations by J. Baker, P. G·avruta, R. Badora and R. Ger, and G.H. Kim.
9
DETERMINANTS AND TRACES FOR THE COMMUTING OPERATORS ON A FINITE VECTOR SPACE
Sung, Myung ;
Korean Journal of Mathematics, volume 16, issue 1, 2008, Pages 115~122
Abstract
In the present article, we give a set of axioms for deter minants and traces of the ltuples of commuting operators on a fixed ¯nite dimensional vector space over a field when l
2. We describe them with or without a coherence assumption especially when
is the field of real numbers. Under the coherence assumption, it turns out that there are only a trivial determinant and trace over arbitrary field
. This leads us to formulate a more appropriate definition of the determinants. In this case, the set of determinants can be de scribed in terms of the Milnor's Ktheory. As for the traces, it is not clear to us how to correctly formulate a definition except for certain cases.