• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.515-524
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• 2004

We prove the local existence of solution for nonconvex-valued differential inclusion under time-varying state constraints.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.557-567
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• 2004

We prove the sufficient conditions for optimality in differential inclusion problem by using the value function. For this purpose, we assume at first that the value function is locally Lipschitz. Secondly, without this assumption, we use the viability theory.

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.515-530
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• 2011

This paper deals with the existence result of solutions of a second order functional differential inclusion, governed by a class of nonconvex sweeping process, with a nonconvex perturbation.

• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.135-144
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• 2005

We consider the stochastic differential inclusion of the form $dX_t{\in}{\sigma}(t, X_t)dB_t+b(t, X_t)dt$, where ${\sigma}$, b are set-valued maps, B is a standard Brownian motion. We prove that the set of solutions is closed.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1161-1168
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• 2008

We prove a theorem that there exists at least a solution reaching the prescribed target in autonomous differential inclusion. A weak invariance theorem is obtained from this theorem as its corollary. To deduce the conclusion, we assume that the target satisfies inward pointing condition. This condition will be given by proximal normal cone.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.807-816
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• 2007

For the stochastic differential inclusion on infinite dimensional space of the form $dX_t{\in}\sigma(X_t)dW_t+b(X_t)dt$, where ${\sigma}$, b are set-valued maps, W is an infinite dimensional Hilbert space valued Q-Wiener process, we prove the boundedness and continuity of solutions under the assumption that ${\sigma}$ and b are closed convex set-valued satisfying the Lipschitz property using approximation.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.159-165
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• 2003

We consider the stochastic differential inclusion of the form $dX_t\;\in\;\sigma(t,\;X_t)db_t+b(t,\;X_t)dt$, where $\sigma$, b are set-valued maps, B is a standard Brownian motion. We prove the boundedness of solutions under the assumption that $\sigma$ and b satisfy the local Lipschitz property and linear growth.

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.537-555
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• 2015

This paper is concerned with the existence of solutions to the following fractional differential inclusion $$\{-{\frac{d}{dx}}\(p_0D^{-{\beta}}_x(u^{\prime}(x)))+q_xD^{-{\beta}}_1(u^{\prime}(x))\){\in}{\partial}F_u(x,u),\;x{\in}(0,1),\\u(0)=u(1)=0,$$ where $_0D^{-{\beta}}_x$ and $_xD^{-{\beta}}_1$ are left and right Riemann-Liouville fractional integrals of order ${\beta}{\in}(0,1)$ respectively, 0 < p = 1 - q < 1 and $F:[0,1]{\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ is locally Lipschitz with respect to the second variable. Due to the general assumption on the constants p and q, the problem does not have a variational structure. Despite that, here we study it combining with an iterative technique and nonsmooth critical point theory, we obtain an existence result for the above problem under suitable assumptions. The result extends some corresponding results in the literatures.

• Nonlinear Functional Analysis and Applications
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• v.29 no.3
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• pp.739-751
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• 2024

In this paper, we study the existence and uniqueness of solutions for a class of fractional differential inclusion including a maximal monotone operator in real space with an initial condition. The main results of the existence and uniqueness are obtained by using resolvent operator techniques and multivalued fixed point theory.

• Journal of Electrical Engineering and Technology
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• v.9 no.1
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• pp.45-51
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• 2014

Distribution system is a critical link between customer and utility. The control of power loss is the main factor which decides the performance of the distribution system. There are two methods such as (i) distribution system reconfiguration and (ii) inclusion of capacitor banks, used for controlling the real power loss. Considering the improvement in voltage profile with the power loss reduction, later method produces better performance than former method. This paper presents an advanced evolutionary algorithm for capacitor inclusion for loss reduction. The conventional sensitivity analysis is used to find the optimal location for the capacitors. In order to achieve a better approximation for the current candidate solution, Opposition based Differential Evolution (ODE) is introduced. The effectiveness of the proposed technique is validated through 10, 33, 34 and85-bus radial distribution systems.