2003 Fiscal Year Final Research Report Summary
Qualitative Theory on Oscillation of Solutions of Differential Equations
| Project/Area Number |
14540162
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Toyama University |
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Principal Investigator |
YOSHIDA Norio Toyama University, Facuty of Science, Professor, 理学部, 教授 (80033934)
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| Co-Investigator(Kenkyū-buntansha) |
FUJITA Yasuhiro Toyama University, Facuty of Science, Assistant Professor, 理学部, 助教授 (10209067)
IKEDA Hideo Toyama University, Facuty of Science, Professor, 理学部, 教授 (60115128)
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| Project Period (FY) |
2002 – 2003
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| Keywords | differential equations / qualitative theory / partial factional-differential equations / oscillation / zero |
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| Research Abstract |
Various extended results were obtained for qualitative theory on oscillation of solutions of partial functional-differential equations, that is, oscillation theory. Sufficient conditions for every solution of parabolic equations of neutral type to be oscillatory were established. Moreover, oscillation theorems for a generalization of the classical Rosenau-Burgers equation were obtained^Oscillation theory for vector parabolic and hyperbolic equations could be constructed. Neutral hyperbolic equations of discrete type have been treated, but we could make oscillation theory for hyperbolic equations with continuous distributed deviating arguments. Three papers on this subject were submitted for publication. Two of them are joint works with Professor Youshan Tao of Dong Hua University in P.R.China. A paper on tumor which is a joint work was accpted for publication in the journal "Ndnlinearity". Furthermore, a joint paper with Professor Litan Yan of Dong Hua University which treat oscillation theory of characteristic initial value problems for hyperbolic equations of hyperbolic type was submitted for publication. I have given an invited lecture at the international conference(Conference on Differential Equations and Applications) held in Slovakia. Then I could discuss with Slovakian Mathematicians, and I could cooperate with Professor Jaros(Comenius University) to establish Picone identities and make Sturmian comparison theorems for half-linear elliptic equations with first order terms. I could hold "Toyama Conference on Differential Equations-2003" at Toyama University, and have fruitful discussions about Mathematics with the guest speaker, Professor E. Minchev of Chiba University.
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Research Products
(12 results)
