• 충청수학회지
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• 제34권4호
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• pp.355-368
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• 2021

In this paper, we investigate necessary and sufficient conditions for the approximate controllability for semilinear stochastic functional differential equations with delays in Hilbert spaces without the strict range condition on the controller even though the equations contain unbounded principal operators, delay terms and local Lipschitz continuity of the nonlinear term.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.1035-1044
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• 2021

Existence and uniqueness results for solutions of system of Riemann-Liouville (R-L) fractional differential equations with initial time difference are obtained. Monotone technique is developed to obtain existence and uniqueness of solutions of system of R-L fractional differential equations with initial time difference.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제12권3호
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• pp.139-151
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• 2008

We investigate a three species food chain system with Lotka-Volterra type functional response and impulsive perturbations. We find a condition for the local stability of prey or predator free periodic solutions by applying the Floquet theory and the comparison theorems and show the boundedness of this system. Furthermore, we illustrate some examples.

• Journal of Applied and Pure Mathematics
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• 제6권1_2호
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• pp.71-96
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• 2024

In this paper we present many interesting results such as completeness and composition theorems in the 𝛼 norm. Moreover, under some conditions, we establish the existence and uniqueness of Cⁿ-(𝜇, 𝜈) pseudo-almost automorphic solutions of class r in the 𝛼-norm for some partial functional differential equations in Banach space when the delay is distributed. An example is given to illustrate our results.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.231-244
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• 2007

In this paper, we use measure theory for considering asymptotically stable of an autonomous system [1] of first order nonlinear ordinary differential equations(ODE's). First, we define a nonlinear infinite-horizon optimal control problem related to the ODE. Then, by a suitable change of variable, we transform the problem to a finite-horizon nonlinear optimal control problem. Then, the problem is modified into one consisting of the minimization of a linear functional over a set of positive Radon measures. The optimal measure is approximated by a finite combination of atomic measures and the problem converted to a finite-dimensional linear programming problem. The solution to this linear programming problem is used to find a piecewise-constant control, and by using the approximated control signals, we obtain the approximate trajectories and the error functional related to it. Finally the approximated trajectories and error functional is used to for considering asymptotically stable of the original problem.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.355-364
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• 2008

Under pathological stress stimuli, dynamics of a biological system can be changed by alteration of several components such as functional proteins, ultimately leading to disease state. These dynamics in disease state can be modeled using differential equations in which kinetic or system parameters can be obtained from experimental data. One of the most effective ways to restore a particular disease state of biology system (i.e., cell, organ and organism) into the normal state makes optimization of the altered components usually represented by system parameters in the differential equations. There has been no such approach as far as we know. Here we show this approach with a cardiac hypertrophy model in which we obtain the existence of the optimal parameters and construct an optimal system which can be used to find the optimal parameters.

• 한국수학사학회지
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• 제16권2호
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• pp.117-128
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• 2003

We investigate the origin and recent history for fuzzy equations. And we introduce the existence theorems of solutions for the fuzzy differential equation with infinite delays and fuzzy functional integral equations. We will also recent researches for controllability of sobolev-type semilinear integro-differential fuzzy system.

• 대한수학회지
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• 제35권1호
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• pp.115-126
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• 1998

We study the optimal control problem of system governed by retarded functional differential $$ x'(t) = A_0 x(t) + A_1 x(t - h) + \\ulcorner\ulcorner\ulcorner_{-h}^{0} a(s)A_2 x(t + s)ds + B_0 u(t) $$ in Hilbert space H. After the fundamental facts of retarded system and the description of condition so called a weak backward uniqueness property are established, the technically important maximal principle and the bang-bang principle are given. its corresponding linear system.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.681-696
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• 2011

In this paper, we consider the existence of mild solutions for a certain class of nonlinear impulsive functional evolution integrodifferential equation with nonlocal conditions in Banach spaces. A sufficient condition is established by using Schaefer's fixed point theorem combined with an evolution system. An example is also given to illustrate our result.

• 대한수학회보
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• 제55권2호
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• pp.479-497
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• 2018

This paper deals with an optimal control on semilinear stochastic functional differential equations with Poisson jumps in a Hilbert space. The existence of an optimal control is derived by the solution of proposed system which satisfies weakly sequentially compactness. Also the stochastic maximum principle for the optimal control is established by using spike variation technique of optimal control with a convex control domain in Hilbert space. Finally, an application of retarded type stochastic Burgers equation is given to illustrate the theory.