1988 Fiscal Year Final Research Report Summary
On the theory and applications for the analysis of the non-standard analysis
| Project/Area Number |
62540126
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | MIYAZAKI UNIVERSITY |
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Principal Investigator |
OGATA Akio MIYAZAKI UNIVERSITY, FACULTY OF EDUCATION, PROFESSOR, 教育学部, 教授 (80040921)
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| Co-Investigator(Kenkyū-buntansha) |
YANAGIHARA Niro CHIBA UNIVERSITY, FACILTY OF SCIENCE, PROFESSOR, 理学部, 教授 (70009041)
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| Project Period (FY) |
1987 – 1988
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| Keywords | analysis / partial differential equation / 複素関数論 |
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| Research Abstract |
Inthis research, we have studied the semilinear elliptic boundary value problems of the form.
(E) -sigma<@D6N(/)ij=1@>D6Di(aij(x)Dj)u = f(x,u,vu) in , sigma<@D6n(/)ij=1@>D6aij(x)cos(v,xj)Diu+b(x)=g(x,u) or , Where is an exterior domain in R<@D1N@>D1 and is the smooth boundary of . Our purpose is to study the multiplicity of positive solutions of (E). The main tools to discuss this matter are the concept of degree of the contact of two solutions(O<U<@D4-@>D4【.Itoreq.】U ) of (E) and the constructing a nonlinear operator equation whose fixed points are solutions of (E).
The main result are, when f and g are sublinear in a sense, either (e) has only one positive solution or an infinite number of solutions {ui} such that
U<@D4-@>D4<U<@D21@>D2<U<@D12@>D2<...<Ui<...<U
On the other hand, we have studied the classification problem of continuous families of infinite dimensional linear systems. It is known that there exist "moduli" for finite dimensional controllable and observable systems. We showed here the result fails in the infinited dimensional case, and derive some conditions under which there exist "moduli", i.e., a fine moduli theorem for infinite dimensional systems.
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