Research on difference methods, positive property and related problems of functional equations

• Project/Area Number: 19540168
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: The University of Electro-Communications
• Principal Investigator: NAITO Toshiki The University of Electro-Communications, 電気通信学部, 教授 (60004446)
• Co-Investigator(Kenkyū-buntansha): YAMAGUTI Kohei 電気通信大学, 電気通信学部, 教授 (00175655) ; ITO Hiroya 電気通信大学, 電気通信学部, 准教授 (30211056) ; ISHIDA Haruhisa 電気通信大学, 電気通信学部, 准教授 (80312792) ; FURUMOCHI Tetsuo 島根大学, 総合理工学部, 教授 (40039128) ; NAKAJIMA Fumio 岩手大学, 教育学部, 教授 (20004484) ; MURAKAMI Satoru 岡山理科大学, 理学部, 教授 (40123963) ; SUZUKI Mami 桜美林大学, リベラルアーツ学群, 准教授 (10236010)
• Co-Investigator(Renkei-kenkyūsha): MIYAZAKI Rinko 静岡大学, 工学部, 准教授 (40244660)
• Project Period (FY): 2007 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2007: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
• Keywords: 差分方程式 / 関数微分方程式 / 積分微分方程式 / 周期解 / 正値解 / 漸近安定性 / 高階双曲型偏微分方程式 / 非線形解析的差分方程式 / 周期作用素 / 不動点定理 / 不安定周期解 / 正直解 / 高階線形双曲型方程式 / 非線形差分方程式 / フロッケ理論 / 遅れ差分制御 / ヴオルテラ方程式 / 一様漸近安定 / 2階非線形差分方程式 / 高階線形双曲形方程式 / 周期線形微分方程式 / リャプーノフ数 / 正値半群 / ペロンーフロベニウス / ロバスト安定 / ボルテラ型方程式 / 不変多様体

Research Abstract

周期線形微分方程式の周期写像の反復写像で生成される線形差分方程式の解をスペクトル分解した。応用として周期線形微分方程式の解のリヤプーノフ指数を与えた。周期係数線形差分方程式の場合に拡大し、解のフロッケ表現を得た。線形積分微分方程式の解が正値性を保つ条件を決定し、解のロバスト安定性と漸近安定性のついての条件を得た。周辺研究として差分方程式の周期解の存在、高階双曲型偏微分方程式の解の一意性、非線形解析的差分方程式について新しい結果を得た。

Research Products

• [Journal Article] Periodic solutions of difference equations (2009)
  • Author(s): T. Furumochi, T. Naito
  • Journal Title: Nonlinear Analysis 71 Pages: 2217-2222
  • Peer Reviewed
• [Journal Article] Delayed Feedback方程式とその性質 (2009)
  • Author(s): 宮崎倫子, 内藤敏機, 申正善
  • Journal Title: 数理解析研究所講究録 1637 Pages: 74-86
• [Journal Article] Stability and robust stability of positive linear Volterra difference equations (2009)
  • Author(s): Pham Huu Anh Ngoc, T. Naito, Jong Son Shin, S. Murakami
  • Journal Title: International J. of Robust and Nonlinear Controls 9 Pages: 552-568
  • Peer Reviewed
• [Journal Article] Stabilities with respect to a weight function in Volterra difference equations (2009)
  • Author(s): S. Murakami
  • Journal Title: Advanced Studies in Pure Mathematics 53 Pages: 189-197
  • Peer Reviewed
• [Journal Article] Periodic solutions of periodic difference equations (2009)
  • Author(s): T. Furumochi, M. Muraoka
  • Journal Title: Advanced Studies in Pure Math. 53 Pages: 63-69
  • Peer Reviewed
• [Journal Article] Periodic solutions of periodic difference equations by Schauder's theorem (2009)
  • Author(s): T. Furumochi
  • Journal Title: Cubo Math. J. 11 Pages: 55-63
  • Peer Reviewed
• [Journal Article] Levi conditions to the Gevrey well-posedness for hyperbolic operators of higher order (2009)
  • Author(s): H. Ishida
  • Journal Title: J. Math. Kyoto Univ. 49 Pages: 173-191
  • Peer Reviewed
• [Journal Article] Oscillatory properties for semilinear degenerate hyperbolic equations of second order (2009)
  • Author(s): H. Ishida, Y. Yuzawa
  • Journal Title: J. Math. Anal. Appl. 356 Pages: 624-532
  • Peer Reviewed
• [Journal Article] Analytic solutions of second order nonlinear difference equations all of whose eigenvalues are 1 (2009)
  • Author(s): M. Suzuki
  • Journal Title: Rendiconti del Seminario Mathematics della Universita di Padova 122 Pages: 13-25
  • Peer Reviewed
• [Journal Article] An application model of a nonlinear difference equation whose the all eigenvalues are 1 (2009)
  • Author(s): M. Suzuki
  • Journal Title: 数理解析研究所講究録 1637 Pages: 57-65
• [Journal Article] Periodic solutions of difference equations (2009)
  • Author(s): Tetsuo Furumochi, Toshiki Naito
  • Journal Title: Nonlinear Analysis Theory Methods & Applications VOL. 71 Pages: 2217-2222
  • Peer Reviewed
• [Journal Article] Delayed Feedback方程式とその性質 (2009)
  • Author(s): 宮崎倫子、内藤敏機、申正善
  • Journal Title: 数理解析研究所講究録 1637 Pages: 74-86
• [Journal Article] Stability and robust stability of positive linear Volterra difference equations (2009)
  • Author(s): Ngoc P.H.A., T.Naito, J-S.Shin, S.Murakami
  • Journal Title: International J.of Robust and Nonlinear Controls VOL. 19 Pages: 552-568
  • Peer Reviewed
• [Journal Article] Levi conditions to the Gevrey well-posedness for hyperbolic operators of higher order (2009)
  • Author(s): Haruhisa Ishida
  • Journal Title: J.Math.Kyoto Univ. 49 Pages: 173-191
  • Peer Reviewed
• [Journal Article] Oscillatory properties for semilinear degenerate hyperbolic equations of second order (2009)
  • Author(s): Haruhisa Ishida, Yasuo Yuzawa
  • Journal Title: J.Math.Anal.Appl. 356 Pages: 624-632
  • Peer Reviewed
• [Journal Article] Periodic solutions of periodic difference equations (2009)
  • Author(s): T.Furumochi, M.Muraoka
  • Journal Title: Advanced Studies in Pure Mathematics 53 Pages: 51-57
  • Peer Reviewed
• [Journal Article] Periodic solutions of periodic difference equations by Schauder's theorem (2009)
  • Author(s): T.Furumochi
  • Journal Title: Cubo Mathematical Journal 11 Pages: 55-63
  • Peer Reviewed
• [Journal Article] Stability with respect to a weight function in Volterra difference equations (2009)
  • Author(s): Satoru Murakami
  • Journal Title: Advanced Studies in Pure Mathematics 53 Pages: 189-197
  • Peer Reviewed
• [Journal Article] Analytic solutions of second order nonlinear difference equations all of whose eigenvalues are 1 (2009)
  • Author(s): Mami Suzuki
  • Journal Title: Rendiconti del Seminario Mathematico della Universita di Padova 122 Pages: 13-25
  • Peer Reviewed
• [Journal Article] An application model of a nonlinear difference equation whose the all eigenvalues are 1 (2009)
  • Author(s): Mami Suzuki
  • Journal Title: 数理解析研究所講究録 1637 Pages: 57-65
• [Journal Article] Periodic solutions of periodic difference equations (2009)
  • Author(s): Furumochi T., Muraoka M.
  • Journal Title: Advanced Studies in Pure Mathematics 53 Pages: 63-69
  • Peer Reviewed
• [Journal Article] Pham Huu Anh Ngoc and Jong Son Shin, Representations and asymptotic behavior of solutions to periodic linear difference equations (2008)
  • Author(s): T. Naito
  • Journal Title: Funkcialaj Ekvacioj 51 Pages: 55-80
  • Peer Reviewed
• [Journal Article] Lyapunov exponents of solutions to linear differential equations with periodic forcing functions (2008)
  • Author(s): T. Naito, Pham Huu Anh Ngoc, Jong Son Shin
  • Journal Title: J. Math. Anal. Appl. 342 Pages: 349-353
  • Peer Reviewed
• [Journal Article] On stability and robust stability of positive linear Volterra equations (2008)
  • Author(s): Pham Huu Anh Ngoc, T. Naito, Jong Son Shin, Satoru Murakami
  • Journal Title: SIAM J. Control Optim. 47 Pages: 975-996
  • Peer Reviewed
• [Journal Article] Floquet representaions and asymptotic behavior of solutions to periodic linear difference equations (2008)
  • Author(s): T. Naito, Pham Huu Anh Ngoc, Jong Son Shin
  • Journal Title: Hiroshima Math. J. 38 Pages: 135-154
  • Peer Reviewed
• [Journal Article] Analytic general solutions of nonlinear difference equations (2008)
  • Author(s): M. Suzuki
  • Journal Title: Annali di Matematica Pura ed Applicata 187 Pages: 353-368
  • Peer Reviewed
• [Journal Article] Translation formulae and its applications (2008)
  • Author(s): 内藤敏機, 申正善
  • Journal Title: 数理解析研究所講究録 1582 Pages: 108-117
• [Journal Article] Floquet representations and asymptotic behavior of solutions to periodic difference equations (2008)
  • Author(s): Naito T, Ngoc P. H. A., Shin J. S.
  • Journal Title: Hiroshima Math. J. 38 Pages: 135-154
  • Peer Reviewed
• [Journal Article] Representations and asymptotic behavior of solutions to periodic linear differece equations (2008)
  • Author(s): Naito T., Ngoc P. H. A., Shin J. S.
  • Journal Title: Funkcial. Ekvac. 51 Pages: 55-80
  • Peer Reviewed
• [Journal Article] On stability and robust stability of positive linear Volterra equations (2008)
  • Author(s): Ngoc P. H. A. . Naito T., Shin J. S., Murakami s.
  • Journal Title: SIAM J. Control Optim. 47 Pages: 975-996
  • Peer Reviewed
• [Journal Article] Uniform asymptotic stability and robust stability for positive linear Volterra difference equations in Banach lattices (2008)
  • Author(s): Murakami S. Nagabuchi Y.
  • Journal Title: Advances in Di fference Equations 2008 Pages: 1-15
  • Peer Reviewed
• [Journal Article] Analytic general solutions of nonlinear difference equations (2008)
  • Author(s): Suzuki M.
  • Journal Title: Annali di Matematica Puraed Applicata 187 Pages: 353-368
  • Peer Reviewed
• [Journal Article] Lyapunov exponents of solutions to linear differential equations with periodic forcing functions (2008)
  • Author(s): T. Naito, P.H.A. Ngoc and J.S. Shin
  • Journal Title: J. Math. Anal. Appl. 342 Pages: 349-353
  • Peer Reviewed
• [Journal Article] On stability and robusut stability of positive linear Volterra equations (2008)
  • Author(s): P.H.A. Ngoc, T. Naito, J.S. Shin and S.Murakami
  • Journal Title: SIAM.J. Control Optm. 47 Pages: 975-996
  • Peer Reviewed
• [Journal Article] Characterizations of positive linear Volterra Integro-differential systems (2007)
  • Author(s): T. Naito, S. Murakami, Jong Son Shin, Pham Huu Anh Ngoc
  • Journal Title: Integr. equ. oper. Theory 58 Pages: 255-272
  • Peer Reviewed
• [Journal Article] On stability of a class of positive linear functional difference equations (2007)
  • Author(s): Pham Huu Anh Ngoc, T. Naito, Jong Son Shin
  • Journal Title: Math. Control Signals Syst. 19 Pages: 361-382
  • Peer Reviewed
• [Journal Article] Characterizations of positive linear functional differential equations (2007)
  • Author(s): Pham Huu Anh Ngoc, T. Naito, Jong Son Shin
  • Journal Title: Funkcialaj Ekvacioj 50 Pages: 1-17
  • NAID: 130000140678
  • Peer Reviewed
• [Journal Article] Stability radius of linear parameter-varying systems and appplications (2007)
  • Author(s): Pham Huu Anh Ngoc, T. Naito
  • Journal Title: J. Math. Anal. Appl. 328 Pages: 170-191
  • Peer Reviewed
• [Journal Article] A representation of solutions for periodic linear differential equations (2007)
  • Author(s): 内藤敏機, 申正善
  • Journal Title: 数理解析研究所講究録 1574 Pages: 59-67
• [Journal Article] Stability radii of higher order linear difference systems under multi-perturbations (2007)
  • Author(s): Pham Huu Anh Ngoc, Thai Bao Tran, T. Naito
  • Journal Title: J. Difference Equations and Applications 13 Pages: 15-24
  • Peer Reviewed
• [Journal Article] Stability radii of positive linear functional differential systems in Banach spaces (2007)
  • Author(s): Pham Huu Anh Ngoc, Nguyen Van Minh, T. Naito
  • Journal Title: International J. Evolution Equations 2 Pages: 75-97
  • Peer Reviewed
• [Journal Article] On stability of a class of positive linear functional difference equations (2007)
  • Author(s): P.H.A. Ngoc, T. Naito and J.S. Shin
  • Journal Title: Math. Control Signals Syst. 19 Pages: 361-382
  • Peer Reviewed
• [Presentation] Commutative gain matrices in delayed feedback controls (2009)
  • Author(s): 宮崎倫子、内藤敏機、申正善
  • Organizer: 数理解析研究所、研究集会「現象解析と関数方程式の新展望」
  • Place of Presentation: 京都大学
  • Year and Date: 2009-11-18
• [Presentation] Commutative gain matrices in delayed feedback contorols (2009)
  • Author(s): 宮崎倫子、内藤敏機、申正善
  • Organizer: 数理解析研究所研究集会「現象解析と関数方程式の展望」
  • Place of Presentation: 京都大学理学部
  • Year and Date: 2009-11-18
• [Presentation] 退化双曲型方程式の振動問題について (2009)
  • Author(s): 石田晴久
  • Organizer: 日本数学2009年度秋季総合分科会
  • Place of Presentation: 大阪大学理学部
  • Year and Date: 2009-09-24
• [Presentation] 退化双曲型方程式の振動問題について (2009)
  • Author(s): 石田晴久
  • Organizer: 日本数学会 2009年度秋季総合分科会
  • Place of Presentation: 大阪大学理学部
  • Year and Date: 2009-09-24
• [Presentation] Delayed feedback方程式について (2009)
  • Author(s): 内藤敏機
  • Organizer: 微分方程式研究集会
  • Place of Presentation: 岩手大学教育学部
  • Year and Date: 2009-08-08
• [Presentation] 微分方程式の定性的理論ワークショップ (2009)
  • Author(s): 村上悟
  • Organizer: Uniform asymptotic stability for positive linear Volterra difference equations in Banach lattices
  • Place of Presentation: 大阪府立大学工学部
  • Year and Date: 2009-03-03
• [Presentation] あるDelayed Feedback制御による周期解の安定化問題 (2008)
  • Author(s): 宮崎倫子, 内藤敏機, 申正善
  • Organizer: 研究集会「微分方程式の総合的研究」
  • Place of Presentation: 京都大学
  • Year and Date: 2008-12-20
• [Presentation] あるDelay Feedback 制御による周期解の安定化問題 (2008)
  • Author(s): 宮崎倫子, 内藤敏機, 申 正善
  • Organizer: 研究集会「微分方程式の総合的研究」
  • Place of Presentation: 京都大学
  • Year and Date: 2008-12-20
• [Presentation] Delayed Feedback方程式とその性質 (2008)
  • Author(s): 申正善, 内藤敏機, 宮崎倫子
  • Organizer: 数理解析研究所研究集会「関数方程式のダイナミックスと数理モデル」
  • Place of Presentation: 京都大学
  • Year and Date: 2008-11-05
• [Presentation] Delayed Feedback 方程式とその性質 (2008)
  • Author(s): 申 正善, 内藤敏機, 宮崎 倫子
  • Organizer: RIMS研究集会「関数方程式のダイナミックスと数理モデル」
  • Place of Presentation: 京都大学
  • Year and Date: 2008-11-05
• [Presentation] 固有値が1の非線形差分方程式の応用モデル (2008)
  • Author(s): 鈴木麻美
  • Organizer: 数理解析研究所研究集会「関数方程式のダイナミックスと数理モデル」
  • Place of Presentation: 京都大学
  • Year and Date: 2008-11-04
• [Presentation] 周期解の安定化について (2008)
  • Author(s): 申正善, 内藤敏機, 宮崎倫子
  • Organizer: 札幌医科大学における微分方程式セミナー
  • Place of Presentation: 札幌医科大学
  • Year and Date: 2008-09-02
• [Presentation] 周期解の安定化問題について (2008)
  • Author(s): 申 正善, 内藤敏機, 宮崎 倫子
  • Organizer: 札幌医科大学における微分方程式セミナー
  • Place of Presentation: 札幌医科大学
  • Year and Date: 2008-09-02
• [Presentation] 過去無限の遅れをもつ微分方程式に関する過去 (2008)
  • Author(s): 内藤敏機
  • Organizer: 研究集会「関数方程式の諸問題」
  • Place of Presentation: 千葉大学けやき会館
  • Year and Date: 2008-03-07
• [Presentation] ある線形微分方程式の解の大域的連続性 (2008)
  • Author(s): 申正善、内藤敏機
  • Organizer: 微分方程式の定性的理論ワークショップ
  • Place of Presentation: 徳島大学総合科学部
  • Year and Date: 2008-03-02
• [Presentation] 変換公式とその応用 (2007)
  • Author(s): 申正善、内藤敏機
  • Organizer: 京都大学数理解析研究所研究集会「関数方程式におけるモデリングと複素解析」
  • Place of Presentation: 京都大学
  • Year and Date: 2007-11-06
• [Presentation] Stabilities in positive linear Volterra integrodifferential equations in a Banach lattice (2007)
  • Author(s): 村上悟
  • Organizer: 京都大学数理解析研究所研究集会「関数方程式におけるモデリングと複素解析」
  • Place of Presentation: 京都大学
  • Year and Date: 2007-11-05
• [Presentation] 非線形2連立差分システムの解析解に関して (2007)
  • Author(s): 鈴木麻美
  • Organizer: 京都大学数理解析研究所研究集会「関数方程式におけるモデリングと複素解析」
  • Place of Presentation: 京都大学
  • Year and Date: 2007-11-05
• [Presentation] A representation of solutions of linear differential equations via the difference equations and spectral mapping theorem (2007)
  • Author(s): Toshiki Naito
  • Organizer: Equadiff
  • Place of Presentation: Wien University of Technology
  • Year and Date: 2007-08-07
• [Presentation] A representation of solutions of linear differential equations via the difference equations and spectral mapping theorem (2007)
  • Author(s): Toshiki NAITO
  • Organizer: Equadiff 2007
  • Place of Presentation: Wien University of Technology
  • Year and Date: 2007-08-07