1989 Fiscal Year Final Research Report Summary
Analysis on Oscillatory Property of Solutions of Differential Equations and its Application
| Project/Area Number |
62540085
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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 | Ibaraki University |
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Principal Investigator |
ONOSE Hiroshi Ibaraki University, College of General Education, Professor, 教養部, 教授 (80007559)
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| Project Period (FY) |
1987 – 1989
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| Keywords | Oscillatory / Volterra integral equation |
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| Research Abstract |
In this research, we want to investigate the oscillatory or nonoscillatory properties of solutions of functional differential equations of the form x^<(n)>(t) + a(t)f(x(g(t))) = 0. These properties are important in the science. Here, we consider the case of the functional differential equation x'(t) + SIGMA^^n__p_i(t)|x(g_i(t))|^<alpha> sgn x(g_i(t)) = q(t)x(t) + r(t), alpha > 0 (1) and the Volterra integral equation x(t) = f(t) -*^t_ a(t,s)g(s,x(s))ds. One of the results is THEOREM. Under the proper assumptions on p_i,q, r and g_i, suppose there exist Q such that Q'(t) = r(t)exp(-*^t_ q(u)du), then every solution of (1) is oscillatory.
The other results obtained are printed in the papers listed in references. As its application, we investigate about the case of hazard function and the stochastic integral equations. Finally we make mention of the book in U. S. A. in which the earlier results of us are used as several theorems.
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