• East Asian mathematical journal
• /
• 제30권5호
• /
• pp.631-637
• /
• 2014

In this paper, we construct some results on the existence and regularity for solutions of neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the existence and regularity for solutions of the neutral system by using fractional power of operators and the local Lipschtiz continuity of nonlinear term without using many of the strong restrictions considering in the previous literature.

• Journal of applied mathematics & informatics
• /
• 제27권5_6호
• /
• pp.1435-1446
• /
• 2009

In this paper we investigate the blow up properties of the positive solutions to a semi linear parabolic system with coupled nonlocal sources $u_t={\Delta}u+k_1{\int}_{\Omega}u^{\alpha}(y,t)v^p(y,t)dy,\;v_t={\Delta}_v+k_2{\int}_{\Omega}u^q(y,t)v^{\beta}(y,t)dy$ with non local Dirichlet boundary conditions. We establish the conditions for global and non-global solutions respectively and obtain its blow up set.

• Korean Journal of Mathematics
• /
• 제25권3호
• /
• pp.455-468
• /
• 2017

We prove the existence of multiple solutions for the fourth order nonlinear elliptic problem with fully nonlinear term. Our method is based on the critical point theory; the variation of linking method and category theory.

• 대한수학회지
• /
• 제34권1호
• /
• 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.

• 대한수학회지
• /
• 제54권6호
• /
• pp.1817-1828
• /
• 2017

We give a simple and direct proof of the characterization of positivity preserving semi-flows for ordinary differential systems. The same method provides an abstract result on a class of evolution systems containing reaction-diffusion systems in a bounded domain of ${\mathbb{R}}^n$ with either Neumann or Dirichlet homogeneous boundary conditions. The conditions are exactly the same with or without diffusion. A similar approach gives the optimal result for invariant rectangles in the case of Neumann conditions.

• Korean Journal of Mathematics
• /
• 제14권2호
• /
• pp.259-271
• /
• 2006

We consider a semilinear elliptic boundary value problem with Dirichlet boundary condition $Au+bu^+-au^-=t_{1{\phi}1}+t_{2{\phi}2}$ in ${\Omega}$ and ${\phi}_n$ is the eigenfuction corresponding to ${\lambda}_n(n=1,2,{\cdots})$. We have a concern with the multiplicity of solutions of the equation when ${\lambda}_1$ < a < ${\lambda}_2$ < b < ${\lambda}_3$.

• 한국수학사학회지
• /
• 제16권4호
• /
• pp.107-115
• /
• 2003

The nonlinear fourth order elliptic equations with jumping nonlinearity was modeled by McKenna. We investigate the trends for the researches of the existence of solutions of a fourth order semilinear elliptic boundary value problem with Dirichlet boundary Condition, ${\Delta}^2u{＋}c{\Delta}u=b_1[(u＋1)^{-}1]{＋}b_2u^+$ in ${\Omega}$, where ${\Omega}$ is a bounded open set in $R^N$ with smooth boundary ${\partial}{\Omega}$.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제12권3호
• /
• pp.169-178
• /
• 2005

In this paper we study the existence and local asymptotic limit of the topological Chern-Simons vortices of the CP(1) model in $\mathbb{R}^2$. After reducing to semilinear elliptic partial differential equations, we show the existence of topological solutions using iteration and variational arguments & prove that there is a sequence of topological solutions which converges locally uniformly to a constant as the Chern­Simons coupling constant goes to zero and the convergence is exponentially fast.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제15권3호
• /
• pp.245-257
• /
• 2008

In this paper, we find the sufficient conditions of controllability of semi-linear neutral functional differential evolution equations with non local conditions using by fractional power of operators and Sadovskii's fixed point theorem.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• 제14권2호
• /
• pp.145-153
• /
• 2014

With reasonable control selections on the space of functions, various application models can take the shape of a well-defined control system on mathematics. In the credibility space, controlability management of fuzzy differential equation is as much important issue as stability. This paper addresses exact controllability for fuzzy differential equations in the credibility space in the perspective of Liu process. This is an extension of the controllability results of Park et al. (Controllability for the semilinear fuzzy integro-differential equations with nonlocal conditions) to fuzzy differential equations driven by Liu process.