• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.353-361
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• 2007

In this paper, we prove the existence of multiple solutions for Neumann and periodic problems. Our main tools are recent general multiplicity theorems proposed by B. Ricceri.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제8권1호
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• pp.71-78
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• 2001

In 1984, Johnson[A bounded convergence theorem for the Feynman in-tegral, J, Math. Phys, 25(1984), 1323-1326] proved a bounded convergence theorem for hte Feynman integral. This is the first stability theorem of the Feynman integral as an $L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$ theory. Johnson and Lapidus [Generalized Dyson series, generalized Feynman digrams, the Feynman integral and Feynmans operational calculus. Mem, Amer, Math, Soc. 62(1986), no 351] studied stability theorems for the Feynman integral as an $L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$ theory for the functional with arbitrary Borel measure. These papers treat functionals which involve only a single integral. In this paper, we obtain the stability theorems for the Feynman integral as an $L(L_1 (\mathbb{R}^N), L_{\infty}(\mathbb{R}^{N}))$theory for the functionals which involve double integral with some Borel measures.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제23권1호
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• pp.1-12
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• 2020

In this case study, a professor was observed to investigate use of instructional examples when teaching the Intermediate Value Theorem in a calculus course. Video-recorded lessons were analyzed with constant comparison to video-stimulated recall interviews and field notes. The professor employed multiple instructional examples, which was initiated by students and modified by the professor. The professor asked students to build non-existing examples as an informal proof of the Intermediate Value Theorem and assessment of students' previous knowledge. Use of incorrect examples on instructional purpose can be an appropriate way for formative assessment as well as a bridge between informal and formal proofs in college mathematics.

• East Asian mathematical journal
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• 제31권1호
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• pp.135-144
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• 2015

In this paper we establish several formulas for multiple integral transform of functionals defined on abstract Wiener space. We then use the these results to establish several basic formulas involving multiple convolution products.

• 대한수학회지
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• 제42권6호
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• pp.1311-1322
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• 2005

We consider the several plane sector domains which are bonded together along common edges with vertex at the origin. Such domains appear in electric conducting problem with multi-layered heterogeneous media. Our aim is to give a structure theorem of the singularities of the electric field at the corner. Also, we provide a regularity theorem for the electric field.

• Korean Journal of Mathematics
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• 제23권4호
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• pp.619-630
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• 2015

This paper is devoted to investigate the multiple solutions for a class of the cooperative elliptic system involving subcritical Sobolev exponents on the bounded domain with smooth boundary. We first show the uniqueness and the negativity of the solution for the linear system of the problem via the direct calculation. We next use the variational method and the mountain pass theorem in the critical point theory.

• Korean Journal of Mathematics
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• 제17권4호
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• pp.495-505
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• 2009

By means of Green function and fixed point theorem related with cone theoretic method we show that there exist multiple nonnegative solutions of a Dirichlet problem $$\array{-[p(t)x^{\prime}(t)]^{\prime}={\lambda}q(t)f(x(t)),\;t{\in}I=[0,\;T]\\x(0)=0=x(T)}$$, and a mixed problem $$\array{-[p(t)x^{\prime}(t)]^{\prime}={\mu}q(t)f(x(t)),\;t{\in}I=[0,\;T]\\x^{\prime}(0)=0=x(T)}$$, where ${\lambda}$ and ${\mu}$ are positive parameters.

• Korean Journal of Mathematics
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• 제19권1호
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• pp.101-109
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• 2011

We get a theorem which shows that there exist at least two or three nontrivial weak solutions for the nonlinear parabolic boundary value problem with the variable coefficient jumping nonlinearity. We prove this theorem by restricting ourselves to the real Hilbert space. We obtain this result by approaching the topological method. We use the Leray-Schauder degree theory on the real Hilbert space.

• 대한수학회지
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• 제54권2호
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• pp.359-380
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• 2017

This paper is concerned with a kind of boundary value problem for singular second order differential systems with Laplacian operators. Using a multiple fixed point theorem, sufficient conditions to guarantee the existence of at least three positive solutions of this kind of boundary value problem are established. An example is presented to illustrate the main results.

• Korean Journal of Mathematics
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• 제17권3호
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• pp.299-314
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• 2009

We investigate the multiple nontrivial solutions of the asymmetric beam equation $u_{tt}+u_{xxxx}=b_1[{(u + 2)}^+-2]+b_2[{(u + 3)}^+-3]$ with Dirichlet boundary condition and periodic condition on t. We reduce this problem into a two-dimensional problem by using variational reduction method and apply the Mountain Pass theorem to find the nontrivial solutions of the equation.