• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.1
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• pp.17-28
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• 2013

In this paper, we study the global existence of solutions for the initial value problems for Volterra-Fredholm type functional impulsive integrodifferential equations. Using the Leray-Schauder Alternative, we derive conditions under which a solution exists globally.

• Journal of the Korean Institute of Telematics and Electronics
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• v.22 no.5
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• pp.83-86
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• 1985

An alternative technique (or the numerical solution of Fredholm integral equations of second kind is presented. The approximate solution is obtained by fitting the data in mixed form at knots in the region of the problem. To decrease the error in the numerical solution, cubic B-spline functions which are twice continuously differentiable at knots are employed as basis function. For a given example, the results of this technique are compared with those of Moment method employing pulse functions for basis function and delta functions for test function and found to br in good agreement.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.493-506
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• 2000

Recently the first author and his coworker report a new finite element method for the Poisson equations with homogeneous Dirichlet boundary conditions on a polygonal domain with one re-entrant angle [7], They use the well-known fact that the solution of such problem has a singular representation, deduced a well-posed new variational problem for a regular part of solution and an extraction formula for the so-called stress intensity factor using tow cut-off functions. They use Fredholm alternative an Garding's inequality to establish the well-posedness of the variational problem and finite element approximation, so there is a maximum bound for mesh h theoretically. although the numerical experiments shows the convergence for every reasonable h with reasonable size y imposing a restriction to the support of the extra cut-off function without using Garding's inequality. We also give error analysis with similar results.

• The Pure and Applied Mathematics
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• v.17 no.3
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• pp.257-268
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• 2010

We investigate the existence of the following Dirichlet boundary value problem $({\mid}u'\mid^{p-2}u')'\;+\;(p\;-\;1)[\alpha{\mid}u^+\mid^{p-2}u^+\;-\;\beta{\mid}u^-\mid^{p-2}u^-]$ = (p - 1)h(t), u(0) = u(T) = 0, where p > 1, $\alpha$ > 0, $\beta$ > 0 and ${\alpha}^{-\frac{1}{p}}\;+\;{\beta}^{-\frac{1}{p}}\;=\;2$, $T\;=\;{\pi}_p/{\alpha}^{\frac{1}{p}}$, ${\pi}_p\;=\; \frac{2{\pi}}{p\;sin(\pi/p)}$ and $h\;{\in}\;L^{\infty}$(0,T). The results of this paper generalize some early results obtained in [8] and [9]. Moreover, the method used in this paper is elementary and new.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.189-207
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• 2021

In this paper, we consider the approximate controllability for a class of semilinear integro-differential functional control equations in which nonlinear terms of given equations satisfy quasi-homogeneous properties. The main method used is to make use of the surjective theorems that is similar to Fredholm alternative in the nonlinear case under restrictive assumptions. The sufficient conditions for the approximate controllability is obtain which is different from previous results on the system operator, controller and nonlinear terms. Finally, a simple example to which our main result can be applied is given.