• 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.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.6 no.4
• /
• pp.288-292
• /
• 2006

Many authors have studied several concepts of fuzzy systems. Balasubramaniam and Muralisankar (2004) proved the existence and uniqueness of fuzzy solutions for the semilinear fuzzy integrodifferential equation with nonlocal initial condition. Recently, Park, Park and Kwun (2006) find the sufficient condition of nonlocal controllability for the semilinear fuzzy integrodifferential equation with nonlocal initial condition. In this paper, we study the existence and uniqueness of solutions for the semilinear fuzzy integrodifferential equations with nonlocal condition and forcing term with memory in $E_{N}$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in $E_{N}$.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.16 no.4
• /
• pp.235-242
• /
• 2012

In this paper, we investigate a nonlocal semilinear heat equation with homogeneous Dirichlet boundary condition in a bounded domain, and prove that there exist solutions with positive initial energy that blow up in finite time.

• Journal of the Korean Mathematical Society
• /
• v.37 no.5
• /
• pp.735-749
• /
• 2000

The multiplicity if periodic sloutions of semilinear dissipative hyperbolic equations is treated

• Communications of the Korean Mathematical Society
• /
• v.12 no.4
• /
• pp.921-933
• /
• 1997

An Ambrosetti-Prodi type multiplicity result for periodic-Dirichlet problem to semilinear parabolic equation is treated.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.3
• /
• 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.

• Kyungpook Mathematical Journal
• /
• v.61 no.3
• /
• pp.559-581
• /
• 2021

In this paper, we establish the existence of solutions and the approximate controllability for the semilinear neutral differential control system under natural assumptions such as the local Lipschitz continuity of nonlinear term. First, we deal with the regularity of solutions of the neutral control system using fractional powers of operators. We also consider the approximate controllability for the semilinear neutral control equation, with a control part in place of a forcing term, using conditions for the range of the controller without the inequality condition as in previous results.

• Communications of the Korean Mathematical Society
• /
• v.28 no.3
• /
• pp.559-569
• /
• 2013

The purpose of this paper is to establish existence, uniqueness and a variation of constant formula of solutions for semilinear partial functional differential equations with unbounded delays and nonlinear part involving integro differetial terms.

• Journal of the Chungcheong Mathematical Society
• /
• v.30 no.4
• /
• pp.397-409
• /
• 2017

In this paper, we investigated the extinction, positivity, and decay estimates of the solutions to the initial-boundary value problem of the semilinear parabolic equation with nonlinear gradient source and interior absorption terms by using the integral norm estimate method. We found that the decay estimates depend on the choices of initial data, coefficients and domain, and the first eigenvalue of the Laplacean operator with homogeneous Dirichlet boundary condition plays an important role in the proofs of main results.

• Communications of the Korean Mathematical Society
• /
• v.28 no.4
• /
• pp.751-766
• /
• 2013

We study the existence and long-time behavior of solutions to the following semilinear degenerate parabolic equation on $\mathbb{R}^N$: $$\frac{{\partial}u}{{\partial}t}-div({\sigma}(x){\nabla}u+{\lambda}u+f(u)=g(x)$$, under a new condition concerning a variable non-negative diffusivity ${\sigma}({\cdot})$. Some essential difficulty caused by the lack of compactness of Sobolev embeddings is overcome here by exploiting the tail-estimates method.