2012 Fiscal Year Final Research Report
Study of the solution semigroup for integral equations and related topics
| Project/Area Number |
22540211
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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 | Okayama University of Science |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
HAMAYA Yoshihiro 岡山理科大学, 総合情報学部, 教授 (40228549)
NAGABUCHI Yutaka 岡山理科大学, 理学部, 教授 (60252607)
KAMIYA Shigeyasu 岡山理科大学, 工学部, 教授 (80122381)
TANAKA Satoshi 岡山理科大学, 理学部, 准教授 (90331959)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 積分方程式 / 解半群 / スペクトル / 定数変化法の公式 / 安定性 |
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| Research Abstract |
We studied some qualitative properties of solutions in integral equations. Indeed, for linear integral equations we analyzed some spectral properties for the generator of the associated solution semigroup, and obtained an estimate on the essential spectral radius of the generator. Furthermore, we established a representation formula in the phase space for solutions of nonhomogeneous linear equations. Applying these results, we obtained Massera type results on the existence of bounded solutions, periodic solutions and so on. Also, for nonlinear integral equations we established the principle of linearization which is effectively applicable to stability problems in nonlinear equations.
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