• Korean Journal of Mathematics
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• 제16권3호
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• pp.389-402
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• 2008

We show the existence of at least two solutions for a class of systems of the critical growth nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition. We first show that the system has a positive solution under suitable conditions, and next show that the system has another solution under the same conditions by the linking arguments.

• 호남수학학술지
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• 제31권1호
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• pp.75-85
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• 2009

We show the existence of the nontrivial periodic solution for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition by critical point theory and linking arguments. We investigate the geometry of the sublevel sets of the corresponding functional of the system, the topology of the sublevel sets and linking construction between two sublevel sets. Since the functional is strongly indefinite, we use the linking theorem for the strongly indefinite functional and the notion of the suitable version of the Palais-Smale condition.

• Korean Journal of Mathematics
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• 제19권3호
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• pp.331-342
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• 2011

We consider the multiplicity of the solutions for a class of a system of critical growth beam equations with periodic condition on t and Dirichlet boundary condition $$\{u_{tt}+u_{xxxx}=av+\frac{2{\alpha}}{{\alpha}+{\beta}}u_{+}^{{\alpha}-1}v_{+}^{\beta}+s{\phi}_{00}\;\;in\;(-\frac{\pi}{2},\;\frac{\pi}{2}){\times}R,\\u_{tt}+v_{xxxx}=bu+\frac{2{\alpha}}{{\alpha}+{\beta}}u_{+}^{\alpha}v_{+}^{{\beta}-1}+t{\phi}_{00}\;\;in\;(-\frac{\pi}{2},\;\frac{\pi}{2}){\times}R,$$ where ${\alpha}$, ${\beta}$ > 1 are real constants, $u_+=max\{u,0\}$, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_00=1$ of the eigenvalue problem $u_{tt}+u_{xxxx}={\lambda}_{mn}u$. We show that the system has a positive solution under suitable conditions on the matrix $A=\(\array{0&a\\b&0}\)$, s > 0, t > 0, and next show that the system has another solution for the same conditions on A by the linking arguments.

• Korean Journal of Mathematics
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• 제17권4호
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• pp.473-480
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• 2009

We prove the existence and multiplicity of nontrivial solutions for a fourth order problem ${\Delta}^2u+c{\Delta}u={\alpha}u-{\beta}(u+1)^-$ in ${\Omega}$, ${\Delta}u=0$ and $u=0$ on ${\partial}{\Omega}$, where ${\lambda}_1{\leq}c{\leq}{\lambda}_2$ (where $({\lambda}_i)_{i{\geq}1}$ is the sequence of the eigenvalues of $-{\Delta}$ in$H_0^1({\Omega})$) and ${\Omega}$ is a bounded open set in $R^N$ with smooth boundary ${\partial}{\Omega}$. The results are proved by applying minimax arguments and linking theory.

• Journal of Pharmaceutical Investigation
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• 제38권3호
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• pp.207-215
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• 2008

Drug approval-patent linkage is the practice of linking drug marketing approval to the patent status of the originator's product and not allowing the grant of marketing approval to any third party prior to the expiration of the patent term unless by consent of the patent owner. Article 18.9.5 of Korea-US Free Trade Agreement requires that Korea introduce the linkage system in drug marketing approval. However, Korea is unfamiliar with the linkage system. In addition, there have been lots of arguments over the impacts of this system on Korean pharmaceutical industry and pharmaceutical market in the future. This report investigated the linkage systems of the US and Canada. The US and Canada have implemented drug approval-patent linkage system since 1984 and 1993, respectively. Both countries have patent lists for drug approvalpatent linkage on which originators are required to list patents on substance, product, and use of their drugs. Generic or follow-on drug applicants must contain a certification regarding each patent listed that relates to the referenced drug. If the patent holder files suit for patent infringement within 45 days of notice of application, drug approval is not allowed for several months - 30 months in the US and 24 months in Canada. Both countries have amended their systems after having experienced unexpected results such as listing improper and additional patents, multiple patent litigations and delayed generic entries. After reviewing the US and Canada's experiences, we suggested three principles needed in implementing the system: protecting patent holder's right; promoting generic drug development and marketing; monitoring the process and the effect of the system.