Qualitative theory of integral equation with delay and its application

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400174
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Osaka Prefecture University
• Principal Investigator: Matsunaga Hideaki 大阪府立大学, 工学(系)研究科(研究院), 教授 (40332960)
• Co-Investigator(Renkei-kenkyūsha): Sugie Jitsuro 島根大学, 総合理工学研究科, 教授 (40196720) ; Kabeya Yoshitsugu 大阪府立大学, 工学研究科, 教授 (70252757)
• Research Collaborator: Nguyen Van Minh コロンブス州立大学, 教授 ; Pituk Mihály パンノニア大学, 教授
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 時間遅れ / 積分方程式 / 差分方程式 / 相空間 / 中心多様体 / 特性根解析 / 漸近安定性 / 振動性

Outline of Final Research Achievements

In this research we have established center manifold theorem for autonomous integral equations with infinite delay by means of the variation-of-constants formula in the phase space. As an application, we have analyzed the stability of nonhyperbolic equilibrium of nonlinear integral equations. Also we have presented asymptotic stability conditions for linear integral systems with finite delay, and asymptotic evaluation formulae for nonlinear integral systems with infinite delay. Furthermore we have obtained some necessary and sufficient conditions for asymptotic stability and oscillation of linear delay difference systems.

Free Research Field

数学解析・関数方程式論