• 충청수학회지
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• 제1권1호
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• pp.19-26
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• 1988

In this paper, we calculate the precise estimation of range of a Gateaux differentiable operator, and apply to the existence of a periodic solution of the second order nonlinear differential equation $$z^{{\prime}{\prime}}+Az^{\prime}+G(z)=e(t)=e(t+2{\pi})$$.

• East Asian mathematical journal
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• 제38권1호
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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.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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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.

• 대한수학회보
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• 제55권2호
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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.

• 대한수학회지
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• 제54권5호
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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.

• 대한수학회지
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• 제40권5호
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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.

• Journal of applied mathematics & informatics
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• 제31권3_4호
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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.

• 대한수학회지
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• 제36권2호
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• pp.355-367
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• 1999

We prove the existence of 2N-1 distinct ordered positive solutions of a class of semilinear elliptic Dirichlet boundary value problems on Rn when the forcing term has N distinct positive stable zeros and the coefficient function decaying to the zero at infinity.

• 대한수학회보
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• 제43권3호
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• pp.599-610
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• 2006

The aim of this paper is to give an existence theorem for a strong solution of generalized vector quasi-equilibrium problems of the weak type II due to Hou et al. using the equilibrium existence theorem for 1-person game, and as an application, we shall give a generalized quasivariational inequality.

• 대한수학회보
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• 제31권2호
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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.