• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.461-470
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• 2019

In this note, we consider the growth of solutions to second order and higher order linear complex differential equations on annuli instead of the complex plane. We establish several theorems that are analogues of the results in the complex plane.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1245-1259
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• 2019

In the paper, we study the growth properties of meromorphic solutions of higher order linear differential equations with entire coefficients of [p, q] - ${\varphi}$ order, ${\varphi}$ being a non-decreasing unbounded function and establish some new results which are improvement and extension of some previous results due to Hamani-Belaidi, He-Zheng-Hu and others.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.8
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• pp.1175-1187
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• 1997

Densification behavior and grain growth of zirconia powder compacts are investigated under high temperature. Experimental data are obtained for zirconia powder under pressureless sintering, sinter forging and hot isostatic pressing. The constitutive equations by Kwon et al. are used for diffusional creep and grain growth. The constitutive equations by McMeeking and co-workers are also included to study the effect of power-law creep. These constitutive equations are implemented into a finite element program (ABAQUS) to investigate the friction effect during sinter forging and the canning effect during hot isostatic pressing. The agreements between experimental data and finite element results are very good in pressureless sintering and hot isostatic pressing, but not as good in sinter forging.

• Journal of the Korean Mathematical Society
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• v.49 no.6
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• pp.1123-1138
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• 2012

We study some anisotropic boundary value problems involving variable exponent growth conditions and we establish the existence and multiplicity of weak solutions by using as main argument critical point theory.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.691-699
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• 2009

In this paper, we establish a multiple existence result of T-periodic solutions for the semilinear parabolic boundary value problem with sublinear growth nonlinearities. We adapt sub-supersolution scheme and topological argument based on variational structure of functionals.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.285-297
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• 2013

This paper deals with parabolic equations coupled via nonstandard growth sources, subject to homogeneous Dirichlet boundary conditions. Three kinds of necessary and sufficient conditions are obtained, which determine the complete classifications for non-simultaneous and simultaneous blowup phenomena. Moreover, blowup rates are given.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1229-1243
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• 2011

In this paper we consider a system of N-Laplacian elliptic equations with critical exponential growth. The existence and multiplicity results of solutions are obtained by a limit index method and Trudinger-Moser inequality.

• Journal of Korean Institute of Industrial Engineers
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• v.4 no.2
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• pp.107-118
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• 1978

The paper illustrates a possible application of control theory to an economic growth system. Simultaneous nonlinear system of differential equations has been modeled which is different from the traditional formulation, based on the theory of economic growth for a two-sector (dual) economy. Necessary and sufficient conditions for the existence of the optimal control are derived directly from the Hamiltonian, and the optimal controls are also obtained by solving simultaneous equations. Obtaining the trajectories of the optimal control and state variables, however, should rely on the numerical procedures. Empirical application has been conducted for the case of the Korean economy as an illustration.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1495-1506
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• 2021

The growth of solutions of second order complex differential equations f" + A(z)f' + B(z)f = 0 with transcendental entire coefficients is considered. Assuming that A(z) has a finite deficient value and that B(z) has either Fabry gaps or a multiply connected Fatou component, it follows that all solutions are of infinite order of growth.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1419-1439
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• 2019

In this paper, we consider a class of noncooperative fourth-order elliptic systems involving nonlocal terms and critical growth in a bounded domain. With the help of Limit Index Theory due to Li [32] combined with the concentration compactness principle, we establish the existence of infinitely many solutions for the problem under the suitable conditions on the nonlinearity. Our results significantly complement and improve some recent results on the existence of solutions for fourth-order elliptic equations and Kirchhoff type problems with critical growth.