• Journal of the Korean Mathematical Society
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• v.36 no.2
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• pp.355-367
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• 1999

We prove the existence of 2N-1 distinct ordered positive solutions of a class of semilinear elliptic Dirichlet boundary value problems on Rn when the forcing term has N distinct positive stable zeros and the coefficient function decaying to the zero at infinity.

• Journal of the Korean Mathematical Society
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• v.36 no.2
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• pp.317-332
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• 1999

In this paper we deal with the optimal control problem for the semilinear functional differential equations with unbounded delays. We will also establish the regularity for solutions of the given system. By using the penalty function method we derive the optimal conditions for optimality of an admissible state-control pairs.

• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.439-460
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• 2002

We prove the multiplicity of ordered positive radial solutions for a semilinear elliptic problem defined on an exterior domain. The key argument is to prove the existence of the third solution in presence of two known solutions. For this, we obtain some partial results related to three solutions theorem for certain singular boundary value problems. Proof are mainly based on the upper and lower solutions method and degree theory.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.37-50
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• 2014

Using variational methods, we prove some results on the nonexistence and multiplicity of weak solutions for a class of semilinear elliptic systems of two equations involving Grushin type operators with sign-changing nonlinearities. We also shows that the similar results can be obtained for systems of m equations, where m is arbitrary.

• Korean Journal of Mathematics
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• v.18 no.1
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• pp.87-96
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• 2010

We consider the semilinear biharmonic equation with Dirichlet boundary condition. We give a theorem that there exist at least three nontrivial solutions for the semilinear biharmonic boundary value problem. We show this result by using the critical point theory, the finite dimensional reduction method and the shape of the graph of the corresponding functional on the finite reduction subspace.

• Journal of the Korean Mathematical Society
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• v.39 no.5
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• pp.775-782
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• 2002

In this paper we prove the existence of mild soultions for semilinear differential equations in a Banach space. The results are obtained by using the semigroup theory and the Schaefer fixed point theorem. An example is provided to illustrate the theory.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.63-79
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• 2018

In this paper, we first consider the existence and regularity of solutions of the semilinear control system under natural assumptions such as the local Lipschtiz continuity of nonlinear term. Thereafter, we will also establish the approximate controllability for the equation when the corresponding linear system is approximately controllable.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.557-567
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• 2006

This paper proves the invariability of reachable sets for the linear control system with positive isolated spectrum points in case where the principal operator generates $C_0-semigroup$ and derives the approximate controllability for the semilinear control system by using spectral operators with respect to isolated spectrum points.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.33-55
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• 2005

The temporal discretisation of a moderate semilinear parabolic problem in an abstract setting by the two-step backward differentiation formula with variable step sizes is analysed. Stability as well as optimal smooth data error estimates are derived if the ratios of adjacent step sizes are bounded from above by 1.91.

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