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Weak solutions for the Hamiltonian bifurcation problem
최규흥,정택선 대한수학회 2016 대한수학회보 Vol.53 No.3
We get a theorem which shows the multiple weak solutions for the bifurcation problem of the superquadratic nonlinear Hamiltonian system. We obtain this result by using the variational method, the critical point theory in terms of the $S^{1}$-invariant functions and the $S^{1}$-invariant linear subspaces.
Boundary Value Problem for One-Dimensional Elliptic Jumping Problem with Crossing $n-$eigenvalues
최규흥,정택선 영남수학회 2019 East Asian mathematical journal Vol.35 No.1
Thispaperisdealtwithone-dimensionalellipticjumpingprob- lem with nonlinearities crossing n eigenvalues. We get one theorem which shows multiplicity results for solutions of one-dimensional elliptic bound- ary value problem with jumping nonlinearities. This theorem is that there exist at least two solutions when nonlinearities crossing odd eigenvalues, at least three solutions when nonlinearities crossing even eigenvalues, exactly one solutions and no solution depending on the source term. We obtain these results by the eigenvalues and the corresponding normalized eigen- functions of the elliptic eigenvalue problem and Leray-Schauder degree theory.
INFINITELY MANY SOLUTIONS FOR A CLASS OF THE ELLIPTIC SYSTEMS WITH EVEN FUNCTIONALS
최규흥,정택선 대한수학회 2017 대한수학회지 Vol.54 No.3
We get a result that shows the existence of infinitely many solutions for a class of the elliptic systems involving subcritical Sobolev exponents nonlinear terms with even functionals on the bounded domain with smooth boundary. We get this result by variational method and critical point theory induced from invariant subspaces and invariant functional.
최규흥(Q-Heung Choi),정택선(Tacksun Jung) 세계환단학회 2023 세계환단학회지 Vol.10 No.1
본 연구에서는 조선시대 갑산부의 고지도를 위상수학적 방법, 기하학적 방법, 대역 기하학적 방법으로 분석함으로써 지도가 내포한 실제적 지리내용을 설명하고자 하였다. 위상수학적으로 갑산부 고지도가 가리키는 곳은 현 백두산 북쪽에서 출발하는 송화강 상류 지류와 무송진撫松鎭, 유수진楡樹鎭, 흥삼진興參鎭, 추수향抽水鄕, 북강진北岡鎭, 유수천향楡樹川鄕, 만량진萬良鎭, 선인교진仙人橋鎭, 화수진樺樹鎭, 만강진漫江鎭, 동강진東岡鎭 등의 근방이다. 갑산부 고지도에서 가리키는 지리적 위치는 이처럼 현 백두산 북쪽 지역 송화강 상류지역이며, 이 지역의 강들은 옛 압록강(현 혼강)과 연결되어 있지 않음에도 이 지역의 강들이 옛 압록강으로 흘러간다고 판단한 것은 잘못이다. 이것이 지리에 대한 무지에서 비롯된 것인지 국경을 정함에 있어 편의상 그렇게 생각한 것인지는 알 수 없다. 19세기 프랑스인이 그린 동북아 지도에는 압록강의 상류와 목단강(옛 토문강)의 상류를 맞닿게 그려져 있다(참조: [그림 12]). 이는 국경을 정하기 위해 옛 압록강 상류와 갑산부 강을 연결해서 그린 것으로 판단된다. 우리는 흔히 조선시대 갑산부 고지도에 나타난 갑산부와 혜산진이 현재 북한 압록강 유역의 혜산과 갑산이라고 믿고 있으나 본 논문을 통해 조선 시대 고지도에 나타난 갑산부의 실제 위치는 이러한 우리들의 상식과 차이가 있음을 발견하게 된다. We analysed the old map of Gabsanbu of Chosun by topological method and geometrical method and compared it with the map of the neighborhood of Hyusan, Gabsan of North Korea, and with the map of the neighborhood of Musonghyun, Baeksansi of China. We revealed that the old map of Gabsanbu of Chosun is not the map of the neighborhood of Hyusan, Gabsan of North Korea. We concluded that the old map of Gabsanbu is a topological map of the neighborhood of Musongjin, Liusujin, in Baeksansi of China. We found the real place of the capital of Gabsanbu in the old map of Gabsanbu of Chosun. The real place of the capital of Gabsanbu is changed by Musongjin(撫松鎭), Musonghyun of China. Hyusanjin, Unpagwan, Unryong, Jindong, Heorin, Dongin, Jarin, Ungyee, Jongpo, Cheonbulsa are changed by Lyusujin(楡樹鎭), Heungsamjin(興參鎭), Chusuhyang(抽 水鄕), Bukgangjin(北岡鎭), Lyusucheonhyang(楡樹川鄕), Manlyangjin(萬良鎭), Seoningyojin(仙人橋鎭), Hwasujin(樺樹鎭), Mangangjin(漫江鎭), Donggangjin(東岡 鎭), respectively. We also revealed that Baekdu Mountain of Chosun is not present Baekdu Mountain of North Korea and that Baekdu Mountain of Chosun is Mogong Mountain in north part of Gyungbak Lake(鏡泊湖). Many Koreans have learned and recognized that Gabsanbu of Chosun is not the neighborhood of North Korea Gabsan. After reading this paper they change their old recognitions.
타원형문제에서 앰브로세티-프로디형 문제연구의 최근 역사
최규흥 ( Q-heung Choi ),정택선 ( Tacksun Jung ) 인하대학교 교육연구소 2003 교육문화연구 Vol.9 No.-
이 논문에서 점프가 일어나는 비선형 부분을 갖는 타원형 방정식의 연구 결과들을 역사적인 관점에서 조사하겠다. 위상적 방법에 의한 연구들에 초점을 맞춰서 이들을 조사한다. 한편, 최근 연구로 해의 다중성과 비선형 부분과의 관계도 서술하였다.
A HISTORY OF RESEACHES OF JUMPING PROBLEMS IN ELLIPTIC EQUATIONS
CHOI, Q-HEUNG,JUNG, TACKSUN 江南大學校産學技術硏究所 2002 산학기술연구소논문집 Vol.- No.14
We investigate a history of researches of a nonlinear elliptic equation with jumping nonlinearity, under Dirichlet boundary condition. The investigation will be focussed on the researches by topological methods. We also add recent researches, relations between multiplicity of solutions and source terms of the equation when the nonlinearity crosses two eigenvalues and the source term is generated by three eigenfunctions.
EXISTENCE OF SIX SOLUTIONS OF THE NONLINEAR HAMILTONIAN SYSTEM
정택선,최규흥 호남수학회 2008 호남수학학술지 Vol.30 No.3
We give a theorem of existence of six nontrivial solutions of the nonlinear Hamiltonian system [수식] For the proof of the theorem we use the critical point theory induced from the limit relative category of the torus with three holes and the finite dimensional reduction method.
SOLVABILITY FOR A CLASS OF THE SYSTEM OF THE NONLINEAR SUSPENSION BRIDGE EQUATIONS
정택선,최규흥 호남수학회 2009 호남수학학술지 Vol.31 No.1
We show the existence of the nontrivial periodic so- lution 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 indef- inite, we use the linking theorem for the strongly inde¯nite func- tional and the notion of the suitable version of the Palais-Smale condition.
Uniqueness Results for the Nonlinear Hyperbolic System with Jumping Nonlinearity
정택선,최규흥 호남수학회 2007 호남수학학술지 Vol.29 No.4
We investigate the existence of solutionsu(x;t) for aperturbationb[(+ +1)+ 1] of the hyperbolic system with Dirich-let boundary condition(0.1)L = [( + + 1)+ 1] + f in (2;2) R;L = [( + + 1)+ 1] + f in (2;2) R;where u+ = max fu;0g, ; are nonzero constants. Here; areperiodic functions.