Toward detailed analysis for oscillation and non-oscillation of Nonlinear ordinary differential equations

2009 Fiscal Year Self-evaluation Report

• Project/Area Number: 19740066
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Kumamoto University (2008-2010); Joetsu University of Education (2007)
• Principal Investigator: TANIGAWA Tomoyuki Kumamoto University, 教育学部, 准教授 (10332008)
• Project Period (FY): 2007 – 2010
• Keywords: 関数方程式

Research Abstract

本研究課題の目的は,非線形Sturm-Liouville微分作用素が主要部である非線形常微分方程式の解の振動性と漸近挙動の精密な解析を行い,それを拠り所にして解の全体構造を解明することである.

Research Products

• [Journal Article] Existence of regularly varying solutions with nonzero indices of half-linear differential equations (2010)
  • Author(s): T. Kusano, J. Manojlovi, T. Tanigawa
  • Journal Title: Computers and Mathematics with Applications 59 Pages: 411-425
  • Peer Reviewed
• [Journal Article] Regularly varying solutions of half-linear functional differential equations with retarded arguments (2008)
  • Author(s): Tomoyuki Tanigawa
  • Journal Title: Acta Mathematica Hungarica 120 Pages: 53-78
  • Peer Reviewed
• [Journal Article] Oscillation theorems for differential equations involving even order nonlinear Sturm-Liouville operator (2007)
  • Author(s): Tomoyuki Tanigawa
  • Journal Title: Georgian Mathematical Journal 14 Pages: 737-768
  • Peer Reviewed
• [Journal Article] Comparison theorems for perturbed half-linear Euler differential equations (2007)
  • Author(s): T. Kusano, J. Manojlovic, T. Tanigawa
  • Journal Title: International Journal of Applied Mathematics and Statistic 9 Pages: 77-94
  • Peer Reviewed
• [Journal Article] The asymptotic behavior of solutions of a class of nonlinear second-order differential equations (2007)
  • Author(s): T. Kusano, V. Maric, T. Tanigawa
  • Journal Title: Bulletin of the London Mathematical Society 39 Pages: 413-418
  • Peer Reviewed
• [Presentation] 進みと遅れの変数をもつ2階半分線形微分方程式のKaramata関数解について (2010)
  • Author(s): 谷川智幸
  • Organizer: 振動理論ワークショップ
  • Place of Presentation: 岡山
  • Year and Date: 20100210-20100211
• [Presentation] 一般化されたThomas-Fermi型微分方程式の正則変動関数解について (2009)
  • Author(s): 谷川智幸
  • Organizer: 広島大学における微分方程式セミナー
  • Place of Presentation: 広島大学
  • Year and Date: 20090831-20090901
• [Presentation] Regular variation for functional differential equations (2008)
  • Author(s): Tomoyuki TANIGAWA
  • Organizer: World Congress of Nonlinear Analysts
  • Place of Presentation: Florida, U.S.A.
  • Year and Date: 20080702-20080709
• [Presentation] 2階半分線形関数微分方程式の正則変動関数解の存在について (2008)
  • Author(s): 谷川智幸
  • Organizer: 振動理論ワークショップ
  • Place of Presentation: 福岡
  • Year and Date: 20080210-20080211
• [Presentation] 遅れ型半分線形微分方程式の正則変動関数解について (2007)
  • Author(s): 谷川智幸
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 東北大学
  • Year and Date: 20070921-20070924