• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1465-1472
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• 2009

In This paper we shall study the existence of solutions of nonlinear two point boundary value problems for nonlinear 2nth-order differential equation $y^{(2n)}=f(t,y,y',{\cdots},y^{(2n-1)})$ with the boundary conditions $g_0(y(a),y'(a),{\cdots},y^{2n-3}(a))=0,g_1(y^{(2n-2)}(a),y^{(2n-1)}(a))=0$, $h_o(y(c),y'(c))=0,h_i(y^{(i)}(c),y^{(i+1)}(c))=0(i=2,3,{\cdots},2n-2)$.

• 조명전기설비학회논문지
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• 제12권4호
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• pp.62-69
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• 1998

송변전성비의 비선형영역 운전으로 인하여 발생하는 고조파는 잘 알려져 있지 않으며 이에 대한 연구도 많지 않다. 비선형회로에서 고조파원, 특히 송변전설비의 비선형 운전에 의한 고조파는 근사적으로 비선형 기계진동문 제를 기술하는 Duffing방정식으로 모델링할 수 있다. 본 논문에서는 Duffing방정식을 이용하여 비선형회로에서 고조파 해석올 위한 새로운 해석 기법올 제안하고 기존에 알려진 여러 기법들과 비교하였다. 사례연구를 통하여 제안된 기법과 기존기법을 바교하였으며, 제안된 방법의 활용성을 고찰하였다.

• 호남수학학술지
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• 제45권1호
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• pp.54-70
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• 2023

In this article, we state and prove several new retarded nonlinear integral and integro-differential inequalities of Gronwall-Bellman-Pachpatte type. These inequalities generalize some former famous inequalities and can be used in examining the existence, uniqueness, boundedness, stability, asymptotic behaviour, quantitative and qualitative properties of solutions of nonlinear differential and integral equations. Applications are provided to demonstrate the strength of our inequalities in estimating the boundedness and global existence of the solution to initial value problem for nonlinear integro-differential equation and Volterra type retarded nonlinear equation. This research work will ensure to open the new opportunities for studying of nonlinear dynamic inequalities on time scale structure of varying nature.

• 충청수학회지
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• 제7권1호
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• pp.141-152
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• 1994

We consider a numerical scheme for solving a nonlinear boundary integral equation (BIE) obtained by reformulation the nonlinear boundary value problem (BVP). We give a simple alternative to the standard collocation method for the nonlinear BIE. This method consists of one conventional linear system and another coupled linear system resulting from an auxiliary BIE which is obtained by differentiating both side of the nonlinear interior integral equations. We obtain an analogue BIE through the perturbation of the fundamental solution of Laplace's equation. We procure the super-convergence of approximate solutions.

• 대한수학회보
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• 제40권3호
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• pp.489-501
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• 2003

In this paper we shall consider the nonlinear delay difference equation $\Delta({p_n}{\Deltax_N})\;+\;q_nf(x_{n-\sigma})\;=\;0,\;n\;=\;0,\;1,\;2,\;...$ when (equation omitted). We will establish some sufficient conditions which guarantee that every solution is oscillatory or converges to zero.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.183-194
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• 2004

In this paper, we consider a Levenberg-Marquardt method for the solution of constrained nonlinear equation problems. The global convergence is established even without requiring the existence of an accumulation point. Some numerical tests are also presented.

• East Asian mathematical journal
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• 제29권1호
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• pp.69-82
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• 2013

In this paper we consider a doubly nonlinear Volterra equation related to the Leray-Lions with a nonsmooth kernel. By exploiting a suitable implicit time-discretization technique we obtain the existence of global strong solution.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권2호
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• pp.175-183
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• 2010

Using Darbo's fixed point theorem, we establish the existence of monotone solutions for a nonlinear quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval.

• 한국정보기술응용학회:학술대회논문집
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• 한국정보기술응용학회 2005년도 6th 2005 International Conference on Computers, Communications and System
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• pp.289-291
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• 2005

In this paper, we introduce the backward solution of nonlinear wave equation for denoising. The PDE method is approved about 4 PSNR value compare with any convolution method. In neuro images, denoising process using proposed PDE is good about 0.2% increased Voxel Region.

• Korean Journal of Mathematics
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• 제18권3호
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• pp.299-309
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• 2010

In this paper, we study the first order nonlinear neutral difference equation: $${\Delta}(x(n)+px(n-{\tau}))+f(n,x(n-c),x(n-d))=r(n),\;n{\geq}n_0$$. Using the Banach fixed point theorem, we prove the existence of bounded positive solutions of the equation, suggest Mann iterative schemes of bounded positive solutions, and discuss the error estimates between bounded positive solutions and sequences generated by Mann iterative schemes.