• Journal of applied mathematics & informatics
• /
• v.28 no.3_4
• /
• pp.739-751
• /
• 2010

This article presents the result on existence, uniqueness and stability of mild solution of impulsive stochastic partial neutral functional differential equations under sufficient condition. The results are obtained by using the method of successive approximation.

• The Pure and Applied Mathematics
• /
• v.8 no.2
• /
• pp.137-143
• /
• 2001

In this paper, we study the existence, uniqueness and norm estimate of solutions for the nonlinear delay integro-differential system.

• Honam Mathematical Journal
• /
• v.42 no.4
• /
• pp.821-828
• /
• 2020

In this work, we prove an existence of an inertial manifold for a system of differential equations with a non-self adjoint leading part. The result follows from the existence and uniqueness of negatively bounded solutions. In fact, we show that a sharp spectral condition is sufficient for the proof.

• East Asian mathematical journal
• /
• v.39 no.1
• /
• pp.43-50
• /
• 2023

This paper is concerned with the existence of positive solutions to the second order differential systems with strongly coupled integral boundary value conditions. The fixed point index theorems are used for the main results.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.753-760
• /
• 2013

We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a bounded Lipschitz do-main under Dirichlet boundary condition. We present by a very simple argument that a strong solution exists globally when the product of $L^2$ norms of the initial velocity and the gradient of the initial velocity and $L^{p,2}$, $p{\geq}4$ norm of the forcing function are small enough. Our condition is scale invariant and implies many typical known global existence results for small initial data including the sharp dependence of the bound on the volumn of the domain and viscosity. We also present a similar result in the whole domain with slightly stronger condition for the forcing.

• Journal of Electrical Engineering and Technology
• /
• v.6 no.5
• /
• pp.706-712
• /
• 2011

Necessary and sufficient conditions for the existence of diagonal, block-diagonal, and triangular decoupling controllers in linear multivariable systems for the most general setting are presented. The plant model in this study is sufficiently general to accommodate non-square plant and non-unity feedback cases with one-degree-of-freedom (1DOF) or two-degree-of-freedom (2DOF) controller configuration. The existence condition is described in terms of rank conditions on the coefficient matrices in partial fraction expansions.

• Communications of the Korean Mathematical Society
• /
• v.14 no.2
• /
• pp.301-310
• /
• 1999

This paper is concerned with the existence of positive solution of a semilinear elliptic equation with homogeneous Dirichlet boundary condition.

• 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.

• Journal of the Korean Mathematical Society
• /
• v.44 no.5
• /
• pp.1065-1078
• /
• 2007

We consider initial value problems for the semirelativistic Hartree type equations with cubic convolution nonlinearity $F(u)=(V*{\mid}u{\mid}^2)u$. Here V is a sum of two Coulomb type potentials. Under a specified decay condition and a symmetric condition for the potential V we show the global existence and scattering of solutions.

• East Asian mathematical journal
• /
• v.36 no.5
• /
• pp.605-612
• /
• 2020

We establish the existence of a positive solution to a semipositone system with integral boundary condition for the large value of the parameter involved in the system. We prove our results by using sub and super solution argument.