• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.205-215
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• 2009

Sufficient conditions for the existence of at least one solution of the boundary value problems for higher order nonlinear difference equations $\{{{{{\Delta^n}x(i-1)=f(i,x(i),{\Delta}x(i),{\cdots},\Delta^{n-2}x(i)),i{\in}[1,T+1],\atop%20{\Delta^m}x(0)=0,m{\in}[0,n-3],}\atop%20\Delta^{n-2}x(0)=\phi(\Delta^{n-1}(0)),}\atop%20\Delta^{n-1}x(T+1)=-\psi(\Delta^{n-2}x(T+1))}\$. are established.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.1047-1061
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• 2011

In this paper, a class of second-order boundary value problems with Sturm-Liouville boundary conditions or multi-point conditions is considered. Some existence and uniqueness theorems of positive solutions of the problem are obtained by using monotone iterative technique, the iterative sequences yielding approximate solutions are also given. The results are illustrated with an example.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1213-1222
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• 2012

The aim of this paper is to establish the existence of three solutions for a Sturm-Liouville mixed boundary value problem. The approach is based on multiple critical points theorems.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1243-1254
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• 2009

The inverse scattering problem is investigated for some second order differential equation with a nonlinear spectral parameter in the boundary condition on the half line [0, $\infty$). In the present paper the coefficient of spectral parameter is not a pure imaginary number and the boundary value problem is not selfadjoint. We define the scattering data of the problem, derive the main integral equation and show that the potential is uniquely recovered.

• Journal of the Korean Mathematical Society
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• v.37 no.4
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• pp.545-563
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• 2000

An integral transform with the Bessel function Jv(z) in the kernel is considered. The transform is relatd to a singular Sturm-Liouville problem on a half line. This relation yields a Plancherel's theorem for the transform. A Paley-Wiener-type theorem for the transform is also derived.

• The Korean Journal of Mycology
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• v.23 no.4 s.75
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• pp.348-353
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• 1995

Biodegradability of poly (3-hydroxybutyrate) (PHB) by Penicillium pinophilum was investigated by the modified Sturm Test. The biodegradability measurement by this method was more reproducible than other conventional activated sludge methods. Optimum inoculum size for the PHB biodegradation was 1% (v/v). The degradation appeared to occur not only on the sample surface but also inside the sample because the biodegradation did not increase quite proportionally with the sample surface area. The biodegradation rate increased to an asymptotic value as the nitrogen content in the test medium increased, indicating the nitrogen source was needed for the synthesis of the PHB depolymerase.

• Kyungpook Mathematical Journal
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• v.32 no.2
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• pp.177-182
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• 1992

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.639-650
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• 2018

Finding a solution for the Legendre equation is difficult. Especially if it is as a part of the Laplace equation solving in the electric fields. In this paper, first a problem of the generalized differential transform method (GDTM) is solved by the Sturm-Liouville equation, then the Legendre equation is solved by using it. To continue, the approximate solution is compared with the nth-degree Legendre polynomial for obtaining the inner and outer potential of a sphere. This approximate is more accurate than the previous solutions, and is closer to an ideal potential in the intervals.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.948-951
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• 2004

This paper introduces the two recently developed checking techniques far missed eigenvalues of nonproportionally damped system. The first technique is based on the argument principle. On the other hand, the second one is based on Rombouts' algorithm and Gleyse's theorem, which has been known as the effective and well-proven method. In the paper, the main features of the two techniques are explained and their effectiveness is also investigated by considering a numerical example.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.231-243
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• 2007

The existence of solutions of a class of two-point boundary value problems for higher order differential equations is studied. Sufficient conditions for the existence of at least one solution are established. It is of interest that the nonlinearity f in the equation depends on all lower derivatives, and the growth conditions imposed on f are allowed to be super-linear (the degrees of phases variables are allowed to be greater than 1 if it is a polynomial). The results are different from known ones since we don't apply the Green's functions of the corresponding problem and the method to obtain a priori bound of solutions are different enough from known ones. Examples that can not be solved by known results are given to illustrate our theorems.