• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.933-942
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• 2014

We give a representation of the component of solutions with characteristic multiplier 1 in a periodic linear inhomogeneous continuous system. It follows from this representation that asymptotic behaviors of the component of solutions to the system and to its associated homogeneous system are quite different, though they are similar in the case where the characteristic multiplier is not 1. Moreover, the representation is applicable to linear discrete systems with constant coefficients.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1549-1559
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• 2008

In this paper, the existence and multiplicity of solution of periodic solutions of p-Laplacian boundary value problem are studied by using degree theory and upper and lower solutions method. Some known results are improved.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.1049-1060
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• 2020

We prove rigidity theorems for ancient solutions of geometric flows of immersed submanifolds. Specifically, we find conditions on the second fundamental form that characterize the shrinking sphere among compact ancient solutions for the mean curvature flow in codimension two surfaces, which is different from the conditions of Risa and Sinestrari in [26] and we also remove the condition that the second fundamental form is uniformly bounded when t ∈ (-∞, -1).

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.81-93
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• 2009

Bifurcation method of dynamical systems is employed to investigate exact solitary wave solutions and kink wave solutions in the generalized modified Boussinesq equation. Under some parameter conditions, their explicit expressions are obtained. Some previous results are extended.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.319-324
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• 2009

In a series of papers [3, 4, 5], the author developed the generalized vector variational inequality with operator solutions (in short, GOVVI) by exploiting variational inequalities with operator solutions (in short, OVVI) due to Domokos and $Kolumb\acute{a}n$ [2]. In this note, we give an extension of the previous work [4] in the setting of Hausdorff locally convex spaces. To be more specific, we present an existence of solutions of (GVVI) under the weak pseudomonotonicity introduced in Yu and Yao [7] within the framework of (GOVVI).

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.925-934
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• 2012

In this work the sine-Gordon equation will be examined for multiple soliton solutions. The higher dimensional sine-Gordon equations will be studied for multiple soliton solutions as well. The simplified form of the Hirota's method will be employed to conduct this analytic study.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1433-1451
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• 2014

In this paper we study the existence of multiple periodic solutions of second-order ordinary differential equations. New results of multiplicity of periodic solutions are obtained when the nonlinearity may cross multiple consecutive eigenvalues. The arguments are proceeded by a combination of variational and degree theoretic methods.

• Journal of the Korean Mathematical Society
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• v.40 no.2
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• pp.287-305
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• 2003

Second order necessary optimality condition for properly efficient solutions of a twice differentiable vector optimization problem is given. We obtain a nonsmooth version of the second order necessary optimality condition for properly efficient solutions of a nondifferentiable vector optimization problem. Furthermore, we prove a second order necessary optimality condition for weakly efficient solutions of a nondifferentiable vector optimization problem.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.153-164
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• 2012

In this paper, we study the existence, non-existence, and multiplicity of positive solutions for a coupled telegraph system using the xed-point theorem of cone expansion/compression type, the upper-lowe solutions method, and xed point index theory.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.61-88
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• 2020

In this paper, we investigate the existence of mild solutions for a class of fractional impulsive evolution equation with periodic boundary condition by means of the method of upper and lower solutions and monotone iterative method. Using the theory of Kuratowski measure of noncompactness, a series of results about mild solutions are obtained. Finally, two examples are given to illustrate our results.