• Korean Journal of Mathematics
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• 제16권1호
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• pp.25-40
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• 2008

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.

• 대한수학회보
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• 제49권6호
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• pp.1213-1222
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• 2012

The aim of this paper is to establish the existence of three solutions for a Sturm-Liouville mixed boundary value problem. The approach is based on multiple critical points theorems.

• Korean Journal of Mathematics
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• 제25권1호
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• pp.37-43
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• 2017

We study the existence of positive solutions of second order nonlinear separated boundary value problems of superlinear as well as sublinear type without imposing monotonicity restrictions on the problem. The type of problem investigated cannot be analyzed using the linearization about the trivial solution because either it does not exist (the sublinear case) or is trivial (the superlinear case). The results follow from a known fixed point theorem by noticing that the concavity of the solutions provides an important condition for the applicability of the fixed point result.

• Journal of applied mathematics & informatics
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• 제33권3_4호
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• pp.425-434
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• 2015

In this paper, a two-point fractional boundary value problem at resonance is considered. By using the coincidence degree theory some existence results of solutions are established.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.147-160
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• 2012

In this paper, we establish some sufficient conditions for the existence of positive solutions for a class of multi-point boundary value problem for fractional functional differential equations involving the Caputo fractional derivative. Our results are based on two fixed point theorems. Two examples are also provided to illustrate our main results.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.295-306
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• 2006

In this paper, by using the Krasnoselskii fixed point theorem, we study the existence of 2m or 2m + 1 symmetric positive solutions of fourth-order two point boundary value problem y(4)(t) - f(t, y(t), y"(t))= 0, y(0) = y(1) = y'(0) = y"(1)=0.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1257-1264
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• 2009

In this paper, we study the existence of solutions for three-point boundary value problem at resonance by using the continuation theorem of Mawhin. Some known results are improved.

• 대한수학회보
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• 제34권1호
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• pp.103-114
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• 1997

The asymptotic Dirichlet problem for harmonic functions on a noncompact complete Riemannian manifold has a long history. It is to find the harmonic function satisfying the given Dirichlet boundary condition at infinity. By now, it is well understood [A, AS, Ch, S], when M is a Cartan-Hadamard manifold with sectional curvature $-b^2 \leq K_M \leq -a^2 < 0$. (By a Cartan-Hadamard manifold, we mean a complete simply connected manifold of non-positive sectional curvature.)

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.945-952
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• 2010

In this paper, existence criteria of one solution to a nonlinear first-order periodic boundary value problem of impulsive dynamic equation on time scales are obtained by using the well-known Schaefer fixed-point theorem.

• 대한수학회지
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• 제43권3호
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• pp.659-676
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• 2006

In this paper, we consider three-component reaction-diffusion system. With an integral condition and a global coupling, this system gives us an interesting free boundary problem. We shall examine the occurrence of a Hopf bifurcation and the stability of solutions as the global coupling constant varies. The main result is that a Hopf bifurcation occurs for global coupling and this motion is transferred to the stable motion for strong global coupling.