• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.4
• /
• pp.773-784
• /
• 2010

The existence of solutions in Besov spaces for nonlinear heat equations having transcendental nonlinearity: $$\frac{\partial}{{\partial}t}u-{\Delta}u=F(u)$$ is investigated. In particular, it is proved the local existence and blow-up phenomena of the solutions in Besov spaces for nonlinear heat equations corresponding to two transcendental nonlinear functions $F(u){\equiv}{\mid}u{\mid}e^{u^2}$ and $F(u){\equiv}e^u$ of rapid growth.

• Communications of the Korean Mathematical Society
• /
• v.12 no.2
• /
• pp.305-309
• /
• 1997

In this paper we prove the existence of a special type of multivortex solutions of $SU (N)_g \times U(1)_l$ Chern-Simons model. More specifically we prove existence of solutions of the self-duality equations for $(\Phi(x), j =1, \cdots, N$ has the same zeroes. In this case we find that the equation can be reduced to the single semilinear elliptic partial differential equations studied by Caffarelli and Yang.

• Communications of the Korean Mathematical Society
• /
• v.21 no.2
• /
• pp.273-285
• /
• 2006

In this paper, we shall give an affirmative answer to the question raised by Kim and Tan [1] dealing with generalized vector quasi-variational inequalities which generalize many existence results on (VVI) and (GVQVI) in the literature. Using the maximal element theorem, we derive two theorems on the existence of weak solutions of (GVQVI), one theorem on the existence of strong solution of (GVQVI), and one theorem on strong solution in the 1-dimensional case.

• The Pure and Applied Mathematics
• /
• v.21 no.4
• /
• pp.307-316
• /
• 2014

We prove the existence of the risk-efficient options proposed by Xu [7]. The proof is given by both indirect and direct ways. Schied [6] showed the existence of the optimal solution of equation (2.1). The one is to use the Schied's result. The other one is to find the sequences converging to the risk-efficient option.

• Communications of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.579-600
• /
• 2017

In this paper we consider a semilinear pseudoparabolic equation with polynomial nonlinearity and infinite delay. We first prove the existence and uniqueness of weak solutions by using the Galerkin method. Then, we prove the existence of a compact global attractor for the continuous semigroup associated to the equation. The existence and exponential stability of weak stationary solutions are also investigated.

• Journal of the Korean Mathematical Society
• /
• v.34 no.1
• /
• pp.247-255
• /
• 1997

In this paper, we are concerned with the existence of positive solutions for the boundary value problems of the form; $$(1) u"(t) + q(t)g(u(t)) = 0, 0 < t < 1 $$ $$ u(0) = 0 = u(1), $$ where q is singular at 0 and /or 1.or 1.

• Communications of the Korean Mathematical Society
• /
• v.17 no.4
• /
• pp.593-606
• /
• 2002

We prove local existence and global uniqueness in one dimensional nonlinear hyperbolic inverse problems. The basic key for showing the local existence of inverse solution is the principle of contracted mapping. As an application, we consider a hyperbolic inverse problem with damping term.

• Journal of the Chungcheong Mathematical Society
• /
• v.1 no.1
• /
• pp.19-26
• /
• 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 $$z^{{\prime}{\prime}}+Az^{\prime}+G(z)=e(t)=e(t+2{\pi})$$.

• 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 applied mathematics & informatics
• /
• v.26 no.1_2
• /
• pp.29-44
• /
• 2008

By employing the continuation theorem of coincidence degree theory, we derive a sufficient condition for the existence and attractricity of a positive periodic solution for a generalized predator-prey model with diffussion feedback controls.