• 대한수학회지
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• 제53권1호
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• pp.201-215
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• 2016

In this paper, we consider the following $Schr{\ddot{o}}dinger$-Kirchhoff-type equations $\[a+b\({\int}_{{\mathbb{R}}^N}({\mid}{\nabla}u{\mid}^2+V(x){\mid}u{\mid}^2)dx\)\][-{\Delta}u+V(x)u]=f(x,u)$, in ${\mathbb{R}}^N$. Under certain assumptions on V and f, some new criteria on the existence and multiplicity of nontrivial solutions are established by the Morse theory with local linking and the genus properties in critical point theory. Some results from the previously literature are significantly extended and complemented.

• 대한수학회논문집
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• 제10권1호
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• pp.115-122
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• 1995

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1445-1460
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• 2010

In this paper, a second-order system of multi-point boundary value problems in Banach spaces is investigated. Based on a specially constructed cone and the fixed point theorem of strict-set-contraction operators, the criterion of the existence and multiplicity of positive solutions are established. And two examples demonstrating the theoretic results are given.

• 대한수학회보
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• 제47권6호
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• pp.1235-1250
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• 2010

In this paper we establish the existence of at least three weak solutions for Neumann doubly eigenvalue elliptic systems driven by a ($p_1,\ldots,p_n$)-Laplacian. Our main tool is a recent three critical points theorem of B. Ricceri.

• 대한수학회지
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• 제47권4호
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• pp.845-860
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• 2010

In this paper, using the Nehari manifold approach and some variational techniques, we discuss the multiplicity of positive solutions for the p(x)-Laplacian problems with non-negative weight functions and prove that an elliptic equation has at least two positive solutions.

• Journal of Mechanical Science and Technology
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• 제19권11호
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• pp.2077-2081
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• 2005

A symmetry breaking nonlinear fluid flow in a two-dimensional wall-driven square cavity taking symmetric boundary condition after some transients has been investigated numerically. It has been shown that the symmetry breaking critical Reynolds number is dependent on the time history of the boundary condition. The cavity has at least three stable steady state solutions for Re=300-375, and two stable solutions if Re>400. Also, it has also been showed that a particular solution among several possible solutions can be obtained by a controlled boundary condition.

• 한국수학사학회지
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• 제15권2호
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• pp.141-160
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• 2002

We investigate the history of the research of the existence of periodic solutions of a nonlinear wave equation with jumping nonlinearity, suggested by Mckenna and Lazer (cf. [15]). We also investigate the recent research of it; a relation between multiplicity of solutions and source terms of the equation when the nonlinearity -($bu^+$-$au^-$) crosses eigenvalues and the source term f is generated by eigenfuntions.

• 충청수학회지
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• 제31권2호
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• pp.255-268
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• 2018

We establish the existence and multiplicity of positive solutions to a coupled system of fractional order differential equations satisfying three-point boundary conditions by utilizing Avery-Henderson functional fixed point theorems and under suitable conditions.

• Korean Journal of Mathematics
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• 제16권2호
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• pp.165-172
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• 2008

We investigate the multiplicity of solutions of the nonlinear biharmonic equation with Dirichlet boundary condition,${\Delta}^2u+c{\Delta}u=bu^{+}+s$, in ­${\Omega}$, where $c{\in}R$ and ${\Delta}^2$ denotes the biharmonic operator. We show by degree theory that there exist at least three solutions of the problem.

• 충청수학회지
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• 제20권1호
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• pp.81-95
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• 2007

We are concerned with the multiplicity of solutions of the nonlinear biharmonic equation with Dirichlet boundary condition, ${\Delta}^2u+c{\Delta}u=g(u)$, in ${\Omega}$, where $c{\in}R$ and ${\Delta}^2$ denotes the biharmonic operator. We show that there exists at least three solutions of the above problem under the suitable condition of g(u).