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

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

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

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

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.1
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• pp.1-14
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• 1998

Multiplicity results of doubly-periodic solution for semilinear heat equations having coercive nonlinearity are discussed. Our proofs rely on Mawhin's continuation theorem.

• 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

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.453-467
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• 1997

A transitive permutation representation of a group G is said to be multiplicity-free if all of its irreducible constituents are distinct. The character corresponding to the action is called the permutation character, given by $(1_H)^G$, where H is the stabilizer of a point. Multiplicity-free permutation characters are of interest in the study of centralizer algebras and distance-transitive graphs, and all finite simple groups are known to have such characters. In this article, we extend to the alternating groups the result of J. Saxl who determined the multiplicity-free permutation representations of the symmetric groups. We classify all subgroups H for which $(1_H)^An, n > 18$, is multiplicity-free.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.393-402
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• 2006

We investigate relations between multiplicity of solutions and source terms in a elliptic equation. We have a concerne with a sharp result for multiplicity of a nonlinear Laplacian differential equation.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1309-1331
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• 2019

We study the homogeneous Dirichlet boundary value problem of generalized Laplacian systems with a singular weight which may not be in $L^1$. Using the well-known fixed point theorem on cones, we obtain the multiplicity results of positive solutions under two different asymptotic behaviors of the nonlinearities at 0 and ${\infty}$. Furthermore, a global result of positive solutions for one special case with respect to a parameter is also obtained.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.121-130
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• 2011

We obtain multiplicity results for the biharmonic problem with a variable coefficient semilinear term. We show that there exist at least three solutions for the biharmonic problem with the variable coefficient semilinear term under some conditions. We obtain this multiplicity result by applying the Leray-Schauder degree theory.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.309-312
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• 1997

The dynamic characteristics of a continuous MMA/MA free-radical solution copolymerization reactor were studied. A mathematical model was developed and kinetic parameters which had been estimated in the previous work were used. With this model, bifurcation diagrams were constructed with various parameters as the bifurcation parameter to predict the region of stable operating conditions and to enhance the controller performance. It was shown that the steady-state multiplicity existed over wide ranges of residence time and jacket inlet temperature. Periodic solution branches were found to emanated from Hopf bifurcation points. Under certain conditions isola was also observed, which would result in poor performance of feedback controllers.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1693-1710
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• 2013

In this paper, we consider the biharmonic elliptic systems of the form $$\{{\Delta}^2u=F_u(u,v)+{\lambda}{\mid}u{\mid}^{q-2}u,\;x{\in}{\Omega},\\{\Delta}^2v=F_v(u,v)+{\delta}{\mid}v{\mid}^{q-2}v,\;x{\in}{\Omega},\\u=\frac{{\partial}u}{{\partial}n}=0,\; v=\frac{{\partial}v}{{\partial}n}=0,\;x{\in}{\partial}{\Omega},$$, where ${\Omega}{\subset}\mathbb{R}^N$ is a bounded domain with smooth boundary ${\partial}{\Omega}$, ${\Delta}^2$ is the biharmonic operator, $N{\geq}5$, $2{\leq}q$ < $2^*$, $2^*=\frac{2N}{N-4}$ denotes the critical Sobolev exponent, $F{\in}C^1(\mathbb{R}^2,\mathbb{R}^+)$ is homogeneous function of degree $2^*$. By using the variational methods and the Ljusternik-Schnirelmann theory, we obtain multiplicity result of nontrivial solutions under certain hypotheses on ${\lambda}$ and ${\delta}$.