• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1123-1139
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• 2014

In this work, we investigate the existence of the extremal solutions for a class of fractional partial differential equations with order 1 < ${\alpha}$ < 2 by upper and lower solution method. Using the theory of Hausdorff measure of noncompactness, a series of results about the solutions to such differential equations is obtained.

• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.439-460
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• 2002

We prove the multiplicity of ordered positive radial solutions for a semilinear elliptic problem defined on an exterior domain. The key argument is to prove the existence of the third solution in presence of two known solutions. For this, we obtain some partial results related to three solutions theorem for certain singular boundary value problems. Proof are mainly based on the upper and lower solutions method and degree theory.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.751-758
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• 1995

We prove the existence of solution for a Dirichlet singular boundary value problem. The proofs are based on the method of upper and lower solutions.

• Environmental Engineering Research
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• v.10 no.4
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• pp.174-180
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• 2005

Nano-sized iron was synthesized using borohydride reduction of $Fe^{3+}$ in aqueous solution. A wide range of synthesis conditions including varying concentrations of reagents, reagent feeding rate, and solution pH was applied in an aqueous system under anaerobic condition. The reactivity of nano-sized iron from each synthesis was evaluated by reacting the iron with TCE in batch systems. Evidence obtained from this study suggest the reactivity of iron is strongly dependent on the synthesis solution pH. The iron reactivity increased as solution pH decreased. More rapid TCE reduction was observed for iron samples synthesized from higher initial $Fe^{3+}$ concentration, which resulted in lower solution pH during the synthesis reaction. Faster feeding of $BH_4^-$ solution to the $Fe^{3+}$ solution resulted in lower synthesis solution pH and the resultant iron samples gave higher TCE reduction rate. Lowering the pH of the solution after completion of the synthesis reaction significantly increased reactivity of iron. It is presumed that the increase in the reactivity of iron synthesized at lower pH is due to less precipitation of iron (hydr)oxides or less surface passivation of iron.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1777-1795
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• 2015

In this paper, we establish sufficient conditions for the solution set of parametric generalized vector mixed quasivariational inequality problem to have the semicontinuities such as the inner-openness, lower semicontinuity and Hausdorff lower semicontinuity. Moreover, a key assumption is introduced by virtue of a parametric gap function by using a nonlinear scalarization function. Then, by using the key assumption, we establish condition ($H_h$(${\gamma}_0$, ${\lambda}_0$, ${\mu}_0$)) is a sufficient and necessary condition for the Hausdorff lower semicontinuity, continuity and Hausdorff continuity of the solution set for this problem in Hausdorff topological vector spaces with the objective space being infinite dimensional. The results presented in this paper are different and extend from some main results in the literature.

• Proceedings of the KIPE Conference
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• 2017.07a
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• pp.598-599
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• 2017

In motor application, High efficiency is important. So Design engineer select small gate resistor for lower switching. But There is side effect with small gate resistor. It makes large dv/dt and system request large EMI filter. It makes price increase. This paper introduce about gate drive IC which have solution both of lower loss and EMI issue.

• Korean Journal of Microbiology
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• v.19 no.3
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• pp.121-127
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• 1981

The constituents of molasses and effect of pH precipitate formation in molasses solution, vary according to its producing districts. The formation of precipitation is not so changeable in the range of buffering zone of molasses solution(pH4.3-6.3) in philippine molasses according to the change of pH value. On lower or higher than the range of buffering zone, the precipitation is increased from pH 4.3 to 2.8 and from 6.3 to 8.1, it is decreased when pH value is lower or higher than the pH value range. For molasses clarifying, it had better adjust the pH of molasses solution to neutral or weak alkali range out of the alkai side of the buffering zone, with lime solution. And then, add the calcium super phosphate solution to pH value of alkali side in buffering zone, as much as the pH of clarified molasses solution can reach to middle value in buffering zone. For the equilibrium of pH value on clarifying molasses, it takes plenty of time more than 6 hours.

• Structural Engineering and Mechanics
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• v.24 no.6
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• pp.727-740
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• 2006

A simple plane-strain solution is derived in this paper for the functionally graded multilayered isotropic elastic cylinder under static deformation. The solution is obtained using method of separation of variables and is expressed in terms of the summation of the Fourier series in the circumferential direction. While the solution for order n = 0 corresponds to the axisymmetric deformation, that for n = 2 includes the special deformation frequently utilized in the upper and lower bounds analysis. Numerical results for a three-phase cylinder with a middle functionally graded layer are presented for both axisymmetric (n = 0) and general (n = 2) deformations, under either the traction or displacement boundary conditions on the surface of the layered cylinder. The solution to the general deformation case (n = 2) is further utilized for the first time to find the upper and lower bounds of the effective shear modulus of the layered cylinder with a functionally graded middle layer. These results could be useful in the future study of cylindrical composites where FGMs and/or multilayers are involved.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.1011-1020
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• 2021

In this paper, first order nonlinear Liouville-Caputo fractional differential equations is studied. The existence and uniqueness of a solution are investigated by using Krasnoselskii and Banach fixed point theorems and the method of lower and upper solutions. Finally, an example is given to illustrate our results.

• East Asian mathematical journal
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• v.31 no.5
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• pp.727-735
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• 2015

We introduce the fundamental theorem of upper and lower solutions for a class of singular ($p_1,\;p_2$)-Laplacian systems and give the proof by using the Schauder fixed point theorem. It will play an important role to study the existence of solutions.