• East Asian mathematical journal
• /
• v.35 no.1
• /
• pp.91-98
• /
• 2019

This paper is concerned with the global existence of strong solution for the controlled ode-pde systems. Also, we consider the continuous dependence of solution on the control.

• Honam Mathematical Journal
• /
• v.38 no.3
• /
• pp.583-592
• /
• 2016

In this paper, we consider the global existence of strong solutions to the incompressible Navier-Stokes equations on the cubic domain in $R^3$. While the global existence for arbitrary data remains as an important open problem, we here provide with some new observations on this matter. We in particular prove the global existence result when ${\Omega}$ is a cubic domain and initial and forcing functions are some linear combination of functions of at most two variables and the like by decomposing the spectral basis differently.

• Journal of applied mathematics & informatics
• /
• v.31 no.3_4
• /
• pp.513-522
• /
• 2013

This paper mainly deals with the stochastic control system, the existence and uniqueness of solutions and the behavior of solutions are investigated. Firstly, we obtain sufficient conditions which guarantee the existence and uniqueness of solutions to the stochastic control system. And then, boundedness of the solution to the system is achieved under mean-square linear growth condition.

• Communications of the Korean Mathematical Society
• /
• v.17 no.1
• /
• pp.175-187
• /
• 2002

The existence and uniqueness of steady states for the age structured S-I-R epidemic model is considered. Intercohort form with external force is considered for the force of infection. Existence is obtained for nonvanishing external force of infection. Uniqueness is shown for the case where there is no vertical transmission of the disease.

• Korean Journal of Mathematics
• /
• v.16 no.3
• /
• pp.259-269
• /
• 2008

The non-existence and existence of the positive solution for the generalized cooperation biological model for two species of animals $${\Delta}u+u(a-bu+g(v))=0\;in\;{\Omega}\\{\Delta}v+v(d+h(u)-cv)=0\;in\;{\Omega}\\u=v=0\;on\;{\partial}{\Omega}$$ are investigated. The techniques used in this paper are elliptic theory, upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations.

• East Asian mathematical journal
• /
• v.33 no.3
• /
• pp.323-331
• /
• 2017

In this paper, we consider the existence of positive solutions for eigenvalue problems of nonlinear fractional differential equations with singular weights. We give various conditions on f and apply Krasnoselskii's Cone Fixed Point Theorem. As a result, we obtain several existence and nonexistence results corresponding to ${\lambda}$ in certain intervals.

• Communications of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.1329-1352
• /
• 2020

In this paper we consider a class of nonlinear evolution equations on infinite dimensional Banach spaces driven by vector measures. We prove existence and uniqueness of solutions and continuous dependence of solutions on the control measures. Using these results we prove existence of optimal controls for Bolza problems. Based on this result we present necessary conditions of optimality.

• Honam Mathematical Journal
• /
• v.30 no.3
• /
• pp.411-423
• /
• 2008

In the field of population dynamics and chemical reaction the possibility or the existence of spatially and temporally nonhomogeneous solutions is a very important problem. For last 50 years or so there have been many results on the pattern formation of chemical reaction systems studying reaction systems with or without diffusions to explain instabilities and nonhomogeneous states arising in biological situations. In this paper we study time-dependent properties of a predator-prey system with functional response and give sufficient conditions that guarantee the existence of stable limit cycles.

• Journal of applied mathematics & informatics
• /
• v.37 no.1_2
• /
• pp.53-63
• /
• 2019

In this paper, we show the existence of solution of the neutral stochastic functional differential equations under non-Lipschitz condition, a weakened linear growth condition and a contractive condition. Furthermore, in order to obtain the existence of solution to the equation we used the Picard sequence.

• Journal of applied mathematics & informatics
• /
• v.37 no.5_6
• /
• pp.399-410
• /
• 2019

In the manuscript, we concern with the existence of solutions of boundary value problems for fourth order nonlinear discrete systems. Some criteria for the existence of at least one nontrivial solution of the problem are obtained. The proof is mainly based upon the variational method and critical point theory. An example is presented to illustrate the main result.