• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.601-612
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• 2023

The existence of solution of the fractional order differential equations is very important mathematical field. Thus, in this work, we discuss, under some hypothesis, the existence of a positive solution for the nonlinear fourth order fractional boundary value problem which includes the p-Laplacian transform. The proposed method in the article is based on the fixed point theorem. More precisely, Krasnosilsky's theorem on a fixed point and some properties of the Green's function were used to study the existence of a solution for fourth order fractional boundary value problem. The main theoretical result of the paper is explained by example.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.877-882
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• 2010

In this paper, a third-order three-point boundary value problem on time scales is considered. We establish criteria for the existence of a solution and a positive solution by using the Leray-Schauder fixed point theorem. An example is also given to illustrate our results.

• East Asian mathematical journal
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• v.38 no.1
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• pp.21-31
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• 2022

This paper is concerned with the optimal control problem associated to the self-organizing target detection model in 1D domains. That is, we show the global existence of weak solution and the existence of optimal control.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1573-1594
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• 2017

This paper deals with the existence and energy estimates of solutions for a class of degenerate nonlocal problems involving sub-linear nonlinearities, while the nonlinear part of the problem admits some hypotheses on the behavior at origin or perturbation property. In particular, for a precise localization of the parameter, the existence of a non-zero solution is established requiring the sublinearity of nonlinear part at origin and infinity. We also consider the existence of solutions for our problem under algebraic conditions with the classical Ambrosetti-Rabinowitz. In what follows, by combining two algebraic conditions on the nonlinear term which guarantees the existence of two solutions as well as applying the mountain pass theorem given by Pucci and Serrin, we establish the existence of the third solution for our problem. Moreover, concrete examples of applications are provided.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.379-403
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• 2018

In this paper we study the first initial boundary value problem for the 3D Navier-Stokes-Voigt equations with infinite delay. First, we prove the existence and uniqueness of weak solutions to the problem by combining the Galerkin method and the energy method. Then we prove the existence of a compact global attractor for the continuous semigroup associated to the problem. Finally, we study the existence and exponential stability of stationary solutions.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.577-594
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• 2013

In this paper, we study the global stability and the existence of almost periodic solution of high-order Hopfield neural networks with distributed delays of neutral type. Some sufficient conditions are obtained for the existence, uniqueness and global exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. An example is given to show the effectiveness of the proposed method and results.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.273-286
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• 2005

Parameter identification problem of a three species (predator, mutualist-prey, and mutualist) ecological system with reaction-diffusion phenomenon is investigated in this paper. The mathematical model of the parameter identification problem is constructed and continuous dependence of the solution for the direct problem on the parameters identified is obtained. Finally, the existence of optimal solution and an optimality necessary condition for the parameter identification problem are given.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.309-318
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• 1994

The approach presented in this paper is based on the transformation of the Stefan problem in one space dimension to an initial-boundary value problem for the heat equation in a fixed domain. Of course, the problem is non-linear. The finite element approximation adopted here is the standared continuous Galerkin method in time. In this paper, only the regular case is discussed. This means the error analysis is based on the assumption that the solution is sufficiently smooth. The aim of this paper is the existence of the solution in a finite Galerkin system of ordinary equations.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.491-506
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• 2019

In this paper, we show the existence and uniqueness of solution to stochastic differential equations under weakened $H{\ddot{o}}lder$ condition and a weakened linear growth condition. Furthermore, the properties of their solutions investigated and estimate for the error between Picard iterations $x_n(t)$ and the unique solution x(t) of SDEs.

• Journal of the Korean Mathematical Society
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• v.40 no.5
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• pp.869-881
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• 2003

In this paper, a nonautonomous predator-prey dispersion delay models with functional response is studied. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for above models is established.