• 대한수학회보
• /
• 제37권4호
• /
• pp.697-710
• /
• 2000

We investigate the existence of solutions of the nonlinear heat equation under Dirichlet boundary conditions on $\Omega$ and periodic condition on the variable t, $Lu-D_tu$+g(u)=f(x, t). We also investigate a relation between multiplicity of solutions and the source terms of the equation.

• Journal of applied mathematics & informatics
• /
• 제34권5_6호
• /
• pp.421-434
• /
• 2016

The main aim of this paper is to discuss the difference between the Euler-Maruyama's approximate solutions and the accurate solution to stochastic differential delay equation. To make the theory more understandable, we impose the non-uniform Lipschitz condition and weakened linear growth condition. Furthermore, we give the pth moment continuous of the approximate solution for the delay equation.

• East Asian mathematical journal
• /
• 제29권3호
• /
• pp.327-335
• /
• 2013

In this paper we consider the quadratic matrix equation which can be defined by $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown complex matrix, and A, B and C are $n{\times}n$ given matrices with complex elements. We first introduce a couple of condition numbers of the equation Q(X) and present normwise condition numbers. Finally, we compare the results and some numerical experiments are given.

• 대한수학회보
• /
• 제38권1호
• /
• pp.175-182
• /
• 2001

In this paper we prove the existence and uniqueness of a mild solution of a functional differential equation with nonlocal condition using the semigroup theory and the Banach fixed point principle.

• 호남수학학술지
• /
• 제27권4호
• /
• pp.609-619
• /
• 2005

We are concerned with the multiplicity of solutions of the nonlinear elliptic equation with Dirichlet boundary condition. We reveal the existence of m solutions of the nonlinear elliptic equation by a critical point theory, under some condition.

• Korean Journal of Mathematics
• /
• 제17권2호
• /
• pp.211-218
• /
• 2009

We investigate the multiple solutions for a suspending beam equation with jumping nonlinearity crossing three eigenvalues, with Dirichlet boundary condition and periodic condition. We show the existence of at least six nontrivial periodic solutions for the equation by using the finite dimensional reduction method and the geometry of the mapping.

• Korean Journal of Mathematics
• /
• 제4권1호
• /
• pp.51-64
• /
• 1996

In this paper we investigate the existence of weak solutions of a nonlinear beam equation under Dirichlet boundary condition on the interval $-\frac{\pi}{2}<x<\frac{\pi}{2}$ and periodic condition on the variable $t$, $u_{tt}+u_{xxxx}=p(x,t,u)$. We show that if $p$ satisfies condition $(p_1)-(p_3)$, then the nonlinear beam equation possesses at least one weak solution.

• 충청수학회지
• /
• 제20권1호
• /
• pp.81-95
• /
• 2007

We are concerned with the multiplicity of solutions of the nonlinear biharmonic equation with Dirichlet boundary condition, ${\Delta}^2u+c{\Delta}u=g(u)$, in ${\Omega}$, where $c{\in}R$ and ${\Delta}^2$ denotes the biharmonic operator. We show that there exists at least three solutions of the above problem under the suitable condition of g(u).

• 대한수학회보
• /
• 제51권3호
• /
• pp.681-689
• /
• 2014

In this paper, we investigate the influence of boundary dissipations on decay property of the solutions for a semilinear wave equation with damping and memory condition on the boundary using the multiplier technique.

• 대한수학회지
• /
• 제34권3호
• /
• pp.609-622
• /
• 1997

We investigate the existence of solutions of the nonlinear beam equation under the Dirichlet boundary condition on the interval $-\frac{2}{\pi}, \frac{2}{\pi}$ and periodic condition on the varible t, $Lu + bu^+ -au^- = f(x, t)$, when the jumping nonlinearity crosses the first positive eigenvalue.