• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.1035-1044
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• 2021

Existence and uniqueness results for solutions of system of Riemann-Liouville (R-L) fractional differential equations with initial time difference are obtained. Monotone technique is developed to obtain existence and uniqueness of solutions of system of R-L fractional differential equations with initial time difference.

• Journal of Korean Philosophical Society
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• v.146
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• pp.245-270
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• 2018

In this paper I study the theoretical characteristic of 'Tao' based on Confucianism. Tao, the most widely used keyword in the history of East Asian philosophy, has amassed ever-greater variety of meaning as time has passed and schools divided into more subdivided schools. Among the many attributes of Tao, the most important thing I think is that Tao has a dual structure between 'Tao' and 'Way'. Somewhere to be reached is called 'Tao', and the pathway that leads to the destination is called 'Way'. In other words, 'Tao' is existence itself, and 'Way' is type of existence. 'Tao' can be goal, and 'Way' can be process. 'Tao' has originality, continuance, and honesty as its own traits, while 'Way' has humanity, practice, and dailiness as its traits. After all, in a broad sense, Tao has a dual structure between the existence and the type of existence; 'Tao' and 'Way'. Many philosophers in Western society have also paid attention to this Tao trait. Among them, Heidegger gave his opinion that is closest to the East Asians. I want to explain why the human beings are the existence on the pathway through this paper. The existence(Tao) and the type of existence(Way) cannot be separated. So, there cannot be existence without type, and type of non-existence is useless. From this point of view, 'Tao' can be both existence and type of existence.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.275-283
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• 2013

In this paper we investigate an initial boundary value problem of a logarithmic wave equation. We establish the global existence of weak solutions to the problem by using Galerkin method, logarithmic Sobolev inequality and compactness theorem.

• Korean Journal of Mathematics
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• v.17 no.1
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• pp.103-112
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• 2009

We show the existence of the solutions for the following nonlinear elliptic problem under the Dirichlet boundary condition. To show the existence of the solutions we use the variational formulation.

• Korean Journal of Mathematics
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• v.9 no.2
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• pp.115-121
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• 2001

In this paper, we establish the conditions that a mild C-existence family yields a solution to the abstract Cauchy problem. And we show the relation between mild C-existence family and C-regularized semigroup if the family of linear operators is exponentially bounded and C is a bounded injective linear operator.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.71-85
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• 1997

In this paper we find sufficient conditions of existence of the nonlinear ODE ($P_{\epsilon}$) which is induced by the nonlinear hyperbolic system of conservation laws in several space variables.

• East Asian mathematical journal
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• v.34 no.5
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• pp.651-660
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• 2018

This paper concerned the existence of positive solutions to the second order differential systems with strongly coupled integral boundary value conditions. By using Krasnoselskii fixed point theorem, we prove the existence of positive solutions according to the parameters under the proper nonlinear growth conditions.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.749-757
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• 2015

In this paper, we prove existence of radial positive solutions for the following boundary value problem

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.531-543
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• 2015

We determine interval of two eigenvalues for which there existence and nonexistence of positive solution for a system of even-order dynamic equation on time scales subject to Sturm-Liouville boundary conditions.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1081-1097
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• 2017

In this paper, we consider coupled wave equation of Kirchhoff type in a noncylindrical domain. This work is devoted to prove the existence and uniqueness of global solutions and decay for the energy of solutions.