• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.34-40
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• 2007

Balasubramaniam and Muralisankar (2004) proved the existence and uniqueness of fuzzy solutions for the semilinear fuzzy integrodifferential equations with nonlocal initial condition. Park et al. (2006) found the sufficient condition of this system. Recently, Kwun et al. (2006) proved the existence and uniqueness of solutions for the semilinear fuzzy integrodifferential equations with nonlocal initial conditions and forcing term with memory in $E_N$. In this paper, we study the controllability for this system 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 Mathematical Society
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• v.37 no.5
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• pp.763-777
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• 2000

We investigate the existence of group invariant solutions of the Emden-Fowler equation, - u=$\mid$x$\mid$$\sigma$$\mid$u$\mid$p-1u in B, u=0 on B and u(gx)=u(x) in B for g G. Here B is the unit ball in n 2, 1$\sigma$ 0 and G is a closed subgrop of the orthogonal group. A soultion of the problem is called a G in variant solution. We prove that there exists a G invariant non-radial solution if and only if G is not transitive on the unit sphere.

• Journal of KSNVE
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• v.9 no.6
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• pp.1218-1226
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• 1999

In this paper, the extended Biot's semilinear model was developed. Combining the extended Biot model with the dynamic equation yields the nonlinear wave equation in poproelastic sound absorbing materials. Both perturbation and matching techniques are used to find solutions for nonlinear wave equations. By comparing results between linear and nonlinear wave solutions, characteristics of nonlinear waves in poroelastic sound abosrbing materials have been studied. Nonlinear waves were found to be attenuated faster than the linear ones. A maximum amplitude of the nonlinear wave occurred near its surface boundaries and decay quickly with distance from the surface. It has also been found that, if the amplitudes of linear waves are known at the surface boundaries, those of nonlinear ones can be determined. This will be the basis of finding effects of nonlinearity on the absorption coefficient and the transmission loss.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.737-737
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• 2000

• Honam Mathematical Journal
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• v.19 no.1
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• pp.61-69
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• 1997

• East Asian mathematical journal
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• v.10 no.1
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• pp.135-172
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• 1994

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.751-761
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• 2000

Symmetry properties of positive solutions for semilinear elliptic problems in n are considered. We give a symmetry result for the problem in the feneral case, and then derive various results for certain classes of demilinear elliptic equations. We employ the moving plane method based on the maximum principle on unbounded domains to obtain the result on symmetry.

• Journal of the Korean Mathematical Society
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• v.37 no.1
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• pp.85-109
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• 2000

In this paper, the multiplicity, stability and the structure of classical solutions of semilinear elliptic equations of the form (equation omitted) will be discussed. Here $\Omega$ is a smooth and bounded domain in $R^{n}$ (n $\geq$ 1), f(x,u) = │u│$^{\alpha}$/sgn(u)-h(x), 0 < $\alpha$ < 1, (n $\geq$ 1) and h is a ${\gamma}$- Holder continuous function on $\Omega$ for some 0 < ${\gamma}$ < 1.a}$ < 1.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.757-769
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• 2008

This paper deals with the existence of optimal controls and maximal principles for semilinear evolution equations with the nonlinear term satisfying Lipschitz continuity. We also present the necessary conditions of optimality which are described by the adjoint state corresponding to the linear equations without a condition of differentiability for nonlinear term.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1669-1687
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• 2014

We consider a nonuniformly nonlinear elliptic systems with resonance part and nonlinear Neumann boundary condition on an unbounded domain. Our arguments are based on the minimum principle and rely on a generalization of the Landesman-Lazer type condition.