• Bulletin of the Korean Mathematical Society
• /
• v.51 no.4
• /
• pp.1211-1216
• /
• 2014

In this paper, we study the structure of m-quasi Einstein manifolds when there exists another distinct solution to the (${\lambda}$, n + m)-Einstein equation. In particular, we derive sufficient conditions for the non-existence of such solutions.

• Journal of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.395-405
• /
• 1997

A globality of the Hopf bifurcation in a free boundary problem for a parabolic partial differential equation is investigated in this paper. We shall examine the global behavior of the Hopf critical eigenvalues and and apply the center-index theory to show the globality.

• Honam Mathematical Journal
• /
• v.29 no.4
• /
• pp.543-554
• /
• 2007

In this paper, we prove the stability of a mixed type functional equation f( -x + y + z) + f(x - y + z) + f(x + y - z) = f(x - y) + f(y - z) + f(z - x) + f.(x) + f(y) + f(z).

• Journal of the Chungcheong Mathematical Society
• /
• v.15 no.1
• /
• pp.35-41
• /
• 2002

In this paper, we prove the stability of a Jensen's functional equation on a normed almost linear space.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.2
• /
• pp.337-346
• /
• 2016

Within white noise approach, we study the existence and uniqueness of the solution of an initial value problem for generalized white noise functionals, and then as a corollary we discuss the linear stochastic differential equation associated with a convolution of white noise functionals.

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.1
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.34 no.3
• /
• 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.

• East Asian mathematical journal
• /
• v.19 no.2
• /
• pp.173-187
• /
• 2003

We study decay estimates of the energy for the nonlinear wave equation in the whole space. We note that the method of proof is based on the multiplier technique and on the unique continuation, and no geometrical condition is imposed on the boundary.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.6
• /
• pp.2001-2010
• /
• 2015

In this paper, we give explicit and new identities for the Bernoulli numbers of the second kind which are derived from a non-linear differential equation.

• Journal of the Chungcheong Mathematical Society
• /
• v.14 no.1
• /
• pp.113-122
• /
• 2001

We prove the Hyers-Ulam-Rassias stability of the Jensen's equation in Banach modules over a Banach algebra.