• Journal of applied mathematics & informatics
• /
• v.28 no.3_4
• /
• pp.763-772
• /
• 2010

This paper deals with the existence of triple positive solutions for the nonlinear second-order three-point boundary value problem z"(t)+a(t)f(t, z(t), z'(t))=0, t $\in$ (0, 1), $z(0)={\nu}z(1)\;{\geq}\;0$, $z'(\eta)=0$, where 0 < $\nu$ < 1, 0 < $\eta$ < 1 are constants. f : [0, 1] $\times$ [0, $+{\infty}$) $\times$ R $\rightarrow$ [0, $+{\infty}$) and a : (0, 1) $\rightarrow$ [0, $+{\infty}$) are continuous. First, Green's function for the associated linear boundary value problem is constructed, and then, by means of a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of triple positive solutions to the boundary value problem. The interesting point is that the nonlinear term f is involved with the first-order derivative explicitly.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.4
• /
• pp.855-867
• /
• 2022

This study finds three different solutions (3-Sol's) for the fourth order nonlinear discrete anisotropic equations (DAE) with real parameter. We use the variational method(VM) and 𝜙_p-Laplacian operator (𝜙_p-LO) to prove the main results. In the following paper, we take the parameters λ, 𝜇 such that λ > 0 and 𝜇 ≥ 0 into consideration.

• Journal of Korean Academy of Oral and Maxillofacial Radiology
• /
• v.17 no.1
• /
• pp.197-207
• /
• 1987

This study was undertaken to investigate the relationships between film and processing solution at different processing temperatures. Three kinds of periapical film were used for this study. They included EP-2l film, DF-58, and A film Each film was processed by automatic film processor with RD-Ⅲ X-dol 90, and A processing solutions at 68° 74° 80° 86° and 92°F. Film density was measured with the densitometer, and base plus fog density, film relative speed, film contrast, and subject contrast were evaluated. The following results were obtained; 1. As the processing temperature was increased, base plus density was increased. Inadequate base plus fog densities were obtained with three films in combination with three processing solutions at 92°F. 2. Lowest base plus fog densities were obtained with A film, followed in ascending order by EP-21, and DF-58 film in combination with A or RD-Ⅲ processing solutions. The sequence of base plus fog densities was in ascending order by EP-21, A, and DF-58 film in combination with X-dol 90 processing solution. 3. The sequence of film relative speed values was in ascending order of EP-21, A, and DF-58 film in combination with A and RD-Ⅲ processing solutions, respectively. 4. As the processing temperature was increased, film contrast values was increased. The sequence of film contrast values was in descending order solution. The sequence of film contrast values was in descending order of EP-2l, DF-58, and A film in combination with RD-Ⅲ, X-dol 90 processing solution at 80°F. 5. As the processing temperature was increased, subject contrast was increased. The sequence of subject contrast was in descending order of A, X-dol 90, and RD-Ⅲ processing solution in combination with three films at 80°F. The sequence of subject contrast was in descending order of EP-21, A, and DF-58 film in combination with A processing solution at different processing temperatures.

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

• East Asian mathematical journal
• /
• v.35 no.1
• /
• pp.41-50
• /
• 2019

This paper is dealt with one-dimensional elliptic jumping problem with nonlinearities crossing n eigenvalues. We get one theorem which shows multiplicity results for solutions of one-dimensional elliptic boundary value problem with jumping nonlinearities. This theorem is that there exist at least two solutions when nonlinearities crossing odd eigenvalues, at least three solutions when nonlinearities crossing even eigenvalues, exactly one solutions and no solution depending on the source term. We obtain these results by the eigenvalues and the corresponding normalized eigenfunctions of the elliptic eigenvalue problem and Leray-Schauder degree theory.

• Korean Journal of Mathematics
• /
• v.20 no.3
• /
• pp.361-369
• /
• 2012

We get a theorem which shows the existence of at least six solutions for the semilinear wave equation with nonlinearity crossing three eigenvalues. We obtain this result by the variational reduction method and the geometric mapping defined on the finite dimensional subspace. We use a contraction mapping principle to reduce the problem on the infinite dimensional space to that on the finite dimensional subspace. We construct a three-dimensional subspace with three axes spanned by three eigenvalues and a mapping from the finite dimensional subspace to the one-dimensional subspace.

• Journal of Korean Ophthalmic Optics Society
• /
• v.1 no.2
• /
• pp.13-18
• /
• 1996

In this study, contact lens care solutions were compared to each other for cytotoxic effect on cultured mouse fibroblasts by the use of neutral red(NR) assay. This study tested the cytotoxicity of 12 cleaning solutions, 2 lubricants and 5 multipurpose solutions(MPS) at 1%, 2%, 3% and 5% concentrations. These solutions are manufactured in Korea and foreign countries. The relative cytotoxic comparison of these solutions showed that some of them are toxic, three of the cleaning solutions were especially highly toxic 10 cells, so most fibroblasts were dead at 1% concentration. The toxic cleaning solutions have more components than other solutions. But both lubricants and MPSs are non-cytotoxic 10 cells. Some of these solutions did not have any descriptions or indications. They are very dangerous to eyes. From this study, contact lens care solutions should be tested for cytotoxic effects.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.24 no.4
• /
• pp.9-18
• /
• 1987

The hydrodynamic radiation forces acting on a ship travelling in waves have been conventionally treated by strip theories or by direct three dimensional approaches, most of which have been formulated in frequency domain. If the forward speed of a ship varies with time, or if its path is not a straight line, conventional frequency domain analysis can no more be used, and for these cases time domain analysis may be used. In this paper, formulations are made in time domain with applications to some problems the results of which are known in frequency domain. And the results of both domains are compared to show the characteristics and validity of time domain solutions. The radiation forces acting on a three dimensional body within the framework of a linear theory. If the linearity of entire system is assumed, radiation forces due to arbitrary ship motions can be expressed by the convolution integral of the arbitrary motion velocity and the so called impulse response function. Numerical calculations are done for some bodies of simple shapes and Series-60[$C_B=0.7$] ship model. For all cases, integral equation techniques with transient Green's function are used, and velocity or acceleration potentials are obtained as the solution of the integral equations. In liner systems, time domain solutions are related with frequency domain solutions by Fourier transform. Therefore time domain solutions are Fourier transformed by suitable relations and the results are compared with various frequency domain solutions, which show good agreements.

• Korean Journal of Logic
• /
• v.11 no.2
• /
• pp.127-170
• /
• 2008

This paper aims to present solutions to three intriguing puzzles on causation that Benardete presents by considering the results of infinite series of telescoping events. The main conceptual tool used in the solutions is the notion of collective causation, what many events cause collectively. It is straightforward to apply the notion to resolve two of the three puzzles. It does not seem as straightforward to apply it to the other puzzle. After some preliminary clarifications of the situation that Benardete describes to present the puzzle, however, we can apply the notion to resolve it as well.

• Journal of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.359-380
• /
• 2017

This paper is concerned with a kind of boundary value problem for singular second order differential systems with Laplacian operators. Using a multiple fixed point theorem, sufficient conditions to guarantee the existence of at least three positive solutions of this kind of boundary value problem are established. An example is presented to illustrate the main results.