• Journal of the Korean Mathematical Society
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• v.50 no.3
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• pp.627-639
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• 2013

The goal of this paper is to obtain the regularity and the existence of solutions of a retarded semilinear differential equation with nonlocal condition by applying Schauder's fixed point theorem. We construct the fundamental solution, establish the H$\ddot{o}$lder continuity results concerning the fundamental solution of its corresponding retarded linear equation, and prove the uniqueness of solutions of the given equation.

• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.53-63
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• 2019

In this paper, we show the existence of solution of the neutral stochastic functional differential equations under non-Lipschitz condition, a weakened linear growth condition and a contractive condition. Furthermore, in order to obtain the existence of solution to the equation we used the Picard sequence.

• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.489-499
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• 2004

In this paper, we introduce and study a new system of nonlinear variational inequalities. The existence and uniqueness of solution for this problem are proved and an iterative algorithm for approximating the solution of system of nonlinear variational inequalities is constructed.

• Structural Engineering and Mechanics
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• v.61 no.3
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• pp.381-387
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• 2017

In this paper we investigate the theory of micropolar thermoelastic bodies whose micro-particles possess microtemperatures. We transform the mixed initial boundary value problem into a temporally evolutionary equation on a Hilbert space and after that we prove the existence and uniqueness of the solution. We also approach the study of the continuous dependence of solution upon initial data and loads.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.143-154
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• 2003

Analytical solutions for the viscous Cahn-Hilliard equation are considered. Existence and uniqueness of the solution are shown. The exponential decay of the solution in H$^2$-norm, which is an improvement of the result in Elliott and Zheng[5]. We also compare the early stages of evolution of the viscous Cahn-Hilliard equation with that of the Cahn-Hilliard equation, which has been given as an open question in Novick-Cohen[8].

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.773-784
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• 2010

The existence of solutions in Besov spaces for nonlinear heat equations having transcendental nonlinearity: $$\frac{\partial}{{\partial}t}u-{\Delta}u=F(u)$$ is investigated. In particular, it is proved the local existence and blow-up phenomena of the solutions in Besov spaces for nonlinear heat equations corresponding to two transcendental nonlinear functions $F(u){\equiv}{\mid}u{\mid}e^{u^2}$ and $F(u){\equiv}e^u$ of rapid growth.

• Journal of the Korean Mathematical Society
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• v.41 no.4
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• pp.747-754
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• 2004

In this paper we investigate the existence and uniqueness of almost periodic and pseudo almost periodic solution for nonlinear differential equation with reflection of argument. For the case of almost periodic forced term, we consider the frequency modules of the solutions.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.205-209
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• 2005

In this paper we discuss on the uniquenss of the solution of partial differential equations: (1) $${\frac{{\partial}w}{{\partial}{\bar{z}}}}=F(z,\;w,\;{\frac{{\partial}w}{{\partial}z}}}+G(z,\;w.{\bar{w})$$ in the sobolev space $W_{1,p}(D)$.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1599-1619
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• 2018

In this paper we study the initial value problem of the non-relativistic Vlasov-Darwin system with generalized variables (VDG). We first prove local existence and uniqueness of a nonnegative classical solution to VDG in three space variables, and establish the blow-up criterion. Then we show that it converges to the well-known Vlasov-Poisson system when the light velocity c tends to infinity in a pointwise sense.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.223-240
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• 2011

In this paper, the problem on periodic solutions of the bidirectional associative memory neural networks with both periodic coefficients and periodic time-varying delays is discussed. By using degree theory, inequality technique and Lyapunov functional, we establish the existence, uniqueness, and global asymptotic stability of a periodic solution. The obtained results of stability are less restrictive than previously known criteria, and the hypotheses for the boundedness and monotonicity on the activation functions are removed.