| Budget Amount *help |
¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1988: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1987: ¥700,000 (Direct Cost: ¥700,000)
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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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