Establishment of unified system of oscillation theory concerning zeros of solutions of partial differential equations

• Project/Area Number: 20540159
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: University of Toyama
• Principal Investigator: YOSHIDA Norio 富山大学, 大学院・理工学研究部(理学), 教授 (80033934)
• Co-Investigator(Kenkyū-buntansha): KOBAYASHI Kusuo 富山大学, 大学院・理工学研究部(理学), 教授 (70033925)
• Project Period (FY): 2008 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 振動理論 / 偏微分方程式 / 零点 / Picone 等式 / Sturm 型比較定理 / Picone等式 / 零点定性的理論 / 定性的理論 / Picone(不)等式 / 解

Research Abstract

For half-linear elliptic equations with p-Laplacian we established Picone identities, and moreover, Sturmian comparison theorems and oscillation theorems, and so it seems that we completed the unified system. Furthermore, we proceeded to study about equations with p（x)-Laplacians for which we could get great oscillation results.We could obtain sufficient conditions for every solution of functional hyperbolic equations of more general type to oscillate.

Research Products

• [Journal Article] Oscillation forquasilinear elliptic equations with p(x)-Laplacians in general domains (2013)
  • Author(s): Norio Yoshida
  • Journal Title: Electronic Journal of Differential Equations Volume: 2013, No. 21 Pages: 1-13
  • Peer Reviewed
• [Journal Article] Oscillation for quasilinear elliptic equations with p(x)-Laplacians in general domains (2013)
  • Author(s): Norio Yoshida
  • Journal Title: Electronic Journal of Differential Equations Volume: 2013(No. 21) Pages: 1-13
  • Peer Reviewed
• [Journal Article] Picone-type inequality and Sturmian comparison theorems for quasilinear elliptic operators with p(x)-Laplacians (2012)
  • Author(s): Norio Yoshida
  • Journal Title: Electronic Journal of Differential Equations Volume: 2012,No.01 Pages: 1-9
  • Peer Reviewed
• [Journal Article] Forced oscillation of hyperbolic equations with mixed nonlinearities (2012)
  • Author(s): Yutaka Shoukaku and Norio Yoshida
  • Journal Title: Electronic Journal of Qualitative Theory of Differential Equations Volume: 33 Pages: 1-13
  • Peer Reviewed
• [Journal Article] Eightieth Birthday anniversary of Kusano Takasi (2012)
  • Author(s): R. P. Agarwal, N. Izobov, I. Kiguradze, T. Kiguradze, A. Lomtatidze, N. Partsvania, M. Perestyuk, N. Rozov, M. Tvrdy and Norio Yoshida
  • Journal Title: Memoirs on Differential Equations and Mathematical Physica Volume: 57 Pages: 1-15
  • Peer Reviewed
• [Journal Article] Eightieth Birthday Anniversary of Kusano Takasi (2012)
  • Author(s): Ravi P. Agarwal, Nikolai Izobov, Ivan Kiguradze, Tariel Kiguradze, Alexander Lomtatidze, Nino Partsvania, Mikola Perestyuk, Nikolai Rozov, Milan Tvrdy and Norio Yoshida
  • Journal Title: Memoirs on Differential Equations and Mathematical Physics Volume: 57 Pages: 1-15
  • Peer Reviewed
• [Journal Article] Oscillation criteria for nonlinear neutral hyperbolic equations with functional arguments (2011)
  • Author(s): Yutaka Shoukaku, Ioannis, P. Stavroulakis and Norio Yoshida
  • Journal Title: Nonlinear Oscillations Volume: 14 Pages: 134-148
  • Peer Reviewed
• [Journal Article] Oscillation criteria for half-linear elliptic inequalities with p(x)-Laplacians via Riccati method (2011)
  • Author(s): Norio Yoshida
  • Journal Title: Nonlinear Analysis Volume: 74 Pages: 2563-2575
  • Peer Reviewed
• [Journal Article] Picone identities for half-linear eeliptic operators with p(x)-Laplacians and applications to Sturmian comparison theory (2011)
  • Author(s): Norio Yoshida
  • Journal Title: Nonlinear Analysis Volume: 74 Pages: 5631-5642
  • Peer Reviewed
• [Journal Article] Forced oscillation criteria for quasilinear elliptic inequalities with p(x)-Laplacian via Riccati method (2011)
  • Author(s): Norio Yoshida
  • Journal Title: Toyama Mathematical Journal Volume: 34 Pages: 93-106
  • NAID: 120004702859
  • Peer Reviewed
• [Journal Article] Oscillation criteria for nonlinear neutral hyperbolic equations with functional arguments (2011)
  • Author(s): Yutaka Shoukaku, Ioannis P.Stavroulakis, Norio Yoshida
  • Journal Title: Nonlinear Oscillations Volume: 14 Pages: 130-144
  • Peer Reviewed
• [Journal Article] Picone identities for half-linear elliptic operators with p(x)-Laplacians and applications to Sturmian comparison theory (2011)
  • Author(s): Norio Yoshida
  • Journal Title: Nonlinear Analysis Volume: 74 Issue: 16 Pages: 5631-5642
  • DOI: 10.1016/j.na.2011.05.048
  • NAID: 120003204526
  • Peer Reviewed
• [Journal Article] Forced oscillation criteria for quasilinear elliptic inequalities with p(x)-Laplacians (2011)
  • Author(s): Norio Yoshida
  • Journal Title: Toyama Mathematical Journal Volume: 34 Pages: 93-106
  • Peer Reviewed
• [Journal Article] Forced oscillation criteria forsuperlinear-sublinear ellipticequations via Picone-type inequality (2010)
  • Author(s): Norio Yoshida
  • Journal Title: Journal of Mathematical Analysis and Aplications Volume: 363 Pages: 711-717
  • Peer Reviewed
• [Journal Article] Forced oscillations of half-linearelliptic equations via Picone-typeinequality (2010)
  • Author(s): Norio Yoshida
  • Journal Title: International Journal of DifferentialEquations Pages: 9-9
  • Peer Reviewed
• [Journal Article] Oscillations of nonlinear hyperbolic equations with functional arguments via Riccati method (2010)
  • Author(s): Yutaka Shoukaku and Norio Yoshida
  • Journal Title: Applied Mathematics and Computation Volume: 217 Pages: 143-151
  • Peer Reviewed
• [Journal Article] Sturmian comparison andoscillation theorems forquasilinear elliptic equations with mixed nonlinearities via Picone-type inequality (2010)
  • Author(s): Norio Yoshida
  • Journal Title: Toyama Mathematical Journal Volume: 33 Pages: 21-41
  • Peer Reviewed
• [Journal Article] Forced oscillation criteria for superlinear-sublinear elliptic equations via Picone-type inequality (2010)
  • Author(s): Norio Yoshida
  • Journal Title: Journal of Mathematical Analysis and Aplications 363 Pages: 711-717
  • Peer Reviewed
• [Journal Article] Forced oscillations of half-linear elliptic equations via Picone-type inequality (2010)
  • Author(s): Norio Yoshida
  • Journal Title: International Journal of Differential Equations ID 520486 Pages: 9-9
  • Peer Reviewed
• [Journal Article] Oscillations of nonlinear hyperbolic equations with functional arguments via Riccati method (2010)
  • Author(s): Yutaka Shoukaku, Norio Yoshida
  • Journal Title: Applied Mathematics and Computation 217 Pages: 143-151
  • Peer Reviewed
• [Journal Article] Forced oscillation criteria for superlinear-sublinear elliptic equations via Picone-type inequality (2010)
  • Author(s): Norio Yoshida
  • Journal Title: Journal of Mathematical Analysis and Applications Volume: 363 Pages: 711-717
  • Peer Reviewed
• [Journal Article] Forced oscillations of half-linear elliptic equations via Picone-type inequality (2010)
  • Author(s): Norio Yoshida
  • Journal Title: International Journal of Differential Equations Volume: 2010
  • Peer Reviewed
• [Journal Article] Sturmian comparison and oscillation theorems for quasilinear elliptic equations with mixed nonlinearities (2010)
  • Author(s): Norio Yoshida
  • Journal Title: Toyama Mathematical Journal Volume: 33 Pages: 21-41
  • Peer Reviewed
• [Journal Article] Sturmian comparison and oscillation theorems for a class of half-linear elliptic equations (2009)
  • Author(s): Norio Yoshida
  • Journal Title: Nonlinear Analysis Volume: 71
  • Peer Reviewed
• [Journal Article] A Picone identity for half-linear elliptic equations and its applications to oscillation theory (2009)
  • Author(s): Norio Yoshida
  • Journal Title: Nonlinear Analysis Volume: 71 Pages: 4935-4951
  • Peer Reviewed
• [Journal Article] Sturmian comparison and oscillation theorems for a class of half-linear elliptic equations (2009)
  • Author(s): Norio Yoshida
  • Journal Title: Nonlinear Analysis 71
  • Peer Reviewed
• [Journal Article] A Picone identity for half-linear elliptic equations and its applications to oscillation theory (2009)
  • Author(s): Norio Yoshida
  • Journal Title: Nonlinear Analysis 71 Pages: 4935-4951
  • Peer Reviewed
• [Journal Article] Oscillatory behavior of second orderneutral differential equations withpositive and negative coefficients (2008)
  • Author(s): Jelena Manojlovic, Yutaka Shoukaku,Tomoyuki Tanigawa and Norio Yoshida
  • Journal Title: Applications and Applied Mathematics Volume: 3 Pages: 1-1
  • Peer Reviewed
• [Journal Article] Oscillatory behavior of second order neutral differential equations with positive and negative coefficients (2008)
  • Author(s): Jelena Manojlovic, Yutaka Shoukaku, Tomoyuki Tanigawa, Norio Yoshida
  • Journal Title: Applications and Applied Mathematics 3 Pages: 1-17
  • Peer Reviewed
• [Journal Article] Oscillatory behavior of second order neutral differential equations with positive and negative coefficients (2008)
  • Author(s): Jelena Manojlovic
  • Journal Title: Applications and Applied Mathematics 3 Pages: 1-17
  • Peer Reviewed
• [Journal Article] Sturmian comparison and oscillation theorems for a class of half-linear elliptic equations
  • Author(s): Norio Yoshida
  • Journal Title: Nonlinear Analysis (in press)
  • Peer Reviewed
• [Presentation] Vibrations of Timoshenko beams with Damping and forcing terms (2012)
  • Author(s): Norio Yoshida
  • Organizer: The IEEE International Conference on Industrial Engineering and Engineering Management
  • Place of Presentation: Hong Kong Convention and ExhibitionCenter, P. R. China.
  • Year and Date: 2012-12-11
• [Presentation] p(x)-Laplacian を持つ半分線形楕円型方程式に対する振動定理- via Riccati method - (2012)
  • Author(s): 吉田範夫
  • Organizer: 岐阜大学における微分方程式セミナー
  • Place of Presentation: 岐阜大学柳戸キャンパス
  • Year and Date: 2012-09-08
• [Presentation] Picone identities and oscillationtheory for quasilinear ellipticequations with p(x)-Laplacians (2012)
  • Author(s): Norio Yoshida
  • Organizer: 6th World Congress of Nolinear Analysts
  • Place of Presentation: University of Athens, Greece
  • Year and Date: 2012-06-26
• [Presentation] Picone 等式と Sturm 型比較定理への応用 (2011)
  • Author(s): 吉田範夫
  • Organizer: 富山解析セミナー 2011
  • Place of Presentation: 富山大学理学部数学科
  • Year and Date: 2011-10-08
• [Presentation] p(x)-Laplacianを持つ半分線形楕円型方程式に対するPicone等式とSturm型比較定理への応用 (2011)
  • Author(s): 吉田範夫
  • Organizer: 富山解析セミナー2011
  • Place of Presentation: 富山大学理学部
  • Year and Date: 2011-10-08
• [Presentation] p(x)-Laplacianを持つ半分線形楕円型方程式に対する振動定理-via Riccati method- (2011)
  • Author(s): 吉田範夫
  • Organizer: 岐阜大学における微分方程式セミナー
  • Place of Presentation: 岐阜大学
  • Year and Date: 2011-09-08
• [Presentation] Picone-type inequality and Sturmian Comparison theorems for quasilinear Elliptic operators with p(x)-Laplacians (2011)
  • Author(s): Norio Yoshida
  • Organizer: Equadiff 2011
  • Place of Presentation: Loughborough University, UK
  • Year and Date: 2011-08-01
• [Presentation] Picone-type inequality and Stumian comparison theorems for quasilinear elliptic operators with p(x)-Laplacians (2011)
  • Author(s): Norio Yoshida
  • Organizer: Equadiff 2011
  • Place of Presentation: Loughborough University, UK
  • Year and Date: 2011-08-01
• [Presentation] Picone identities for half-linearelliptic equations with p(x)-Laplacians and applications (2011)
  • Author(s): 吉田範夫
  • Organizer: RIMS 共同研究「異常拡散の数理」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2011-07-17
• [Presentation] Picone 等式と Sturm 型比較定理 (2010)
  • Author(s): 吉田範夫
  • Organizer: 富山解析セミナー 2010
  • Place of Presentation: 富山大学理学部数学科
  • Year and Date: 2010-10-02
• [Presentation] Picone 等式と Sturm 型比較定理 (2010)
  • Author(s): 吉田範夫
  • Organizer: 富山解析セミナー2010
  • Place of Presentation: 富山大学理学部数学科
  • Year and Date: 2010-10-02
• [Presentation] Picone等式とSturm型比較定理 (2010)
  • Author(s): 吉田範夫
  • Organizer: 富山解析セミナー2010
  • Place of Presentation: 富山大学理学部
  • Year and Date: 2010-10-02
• [Presentation] 或る半分線形楕円型方程式に対するPicone 等式と振動定理 (2010)
  • Author(s): 吉田範夫
  • Organizer: 振動理論ワークショップ-倉敷 2010
  • Place of Presentation: 岡山理科大学国際交流センター
  • Year and Date: 2010-02-11
• [Presentation] 或る半分線形楕円型方程式に対するPicone等式と振動定理 (2010)
  • Author(s): 吉田範夫
  • Organizer: 振動理論ワークショップ-倉敷2010
  • Place of Presentation: 岡山理科大学
  • Year and Date: 2010-02-11
• [Presentation] 時間遅れと分枝過程 (2010)
  • Author(s): 小林久壽雄
  • Organizer: 富山解析セミナー 2010
  • Place of Presentation: 富山大学理学部数学科
• [Presentation] 半分線形楕円型方程式に対する Picone等式と Sturm 型比較定理への応用 (2009)
  • Author(s): 吉田範夫
  • Organizer: 富山解析セミナー 2009
  • Place of Presentation: 富山大学理学部数学科
  • Year and Date: 2009-10-03
• [Presentation] ある分枝過程の極限について (2009)
  • Author(s): 小林久壽雄
  • Organizer: 富山解析セミナー 2009
  • Place of Presentation: 富山大学理学部数学科
  • Year and Date: 2009-10-03
• [Presentation] 半分線形楕円型方程式に対する Picone等式と Sturm 型比較定理への応用 (2009)
  • Author(s): 吉田範夫
  • Organizer: 富山解析セミナー2009
  • Place of Presentation: 富山大学理学部数学科
  • Year and Date: 2009-10-03
• [Presentation] ある分枝過程の極限について (2009)
  • Author(s): 小林久壽雄
  • Organizer: 富山解析セミナー2009
  • Place of Presentation: 富山大学理学部数学科
  • Year and Date: 2009-10-03
• [Presentation] 半分線形楕円型方程式に対するPicone等式とSturm型比較定理への応用 (2009)
  • Author(s): 吉田範夫
  • Organizer: 富山解析セミナー2009
  • Place of Presentation: 富山大学理学部
  • Year and Date: 2009-10-03
• [Presentation] 或る半分線形楕円型方程式に対するPicone 等式と Sturm 型比較定理 (2009)
  • Author(s): 吉田範夫
  • Organizer: 広島大学における微分方程式セミナー(通算第32回)
  • Place of Presentation: 広島大学東千田キャンパス
  • Year and Date: 2009-08-31
• [Presentation] 或る半分線形楕円型方程式に対するPicone等式とSturm型比較定理 (2009)
  • Author(s): 吉田範夫
  • Organizer: 広島大学における微分方程式セミナー
  • Place of Presentation: 広島大学東千田キャンパス
  • Year and Date: 2009-08-31
• [Presentation] 半分線形楕円型方程式に対する Picone等式とその応用 (2008)
  • Author(s): 吉田範夫
  • Organizer: 富山解析セミナー 2008
  • Place of Presentation: 富山大学理学部数学科
  • Year and Date: 2008-10-04
• [Presentation] 最終型粒子の分布について (2008)
  • Author(s): 小林久壽雄
  • Organizer: 富山解析セミナー 2008
  • Place of Presentation: 富山大学理学部数学科
  • Year and Date: 2008-10-04
• [Presentation] 半分線形楕円型方程式に対する Picone等式とその応用 (2008)
  • Author(s): 吉田範夫
  • Organizer: 富山解析セミナー2008
  • Place of Presentation: 富山大学理学部数学科
  • Year and Date: 2008-10-04
• [Presentation] 最終型粒子の分布について (2008)
  • Author(s): 小林久壽雄
  • Organizer: 富山解析セミナー2008
  • Place of Presentation: 富山大学理学部数学科
  • Year and Date: 2008-10-04
• [Presentation] 半分線形楕円型方程式に対するPicone等式とその応用 (2008)
  • Author(s): 吉田範夫
  • Organizer: 富山解析セミナー2008
  • Place of Presentation: 富山大学理学部
  • Year and Date: 2008-10-04
• [Presentation] Sturmian comparison and oscillationtheorems for a class of half-linearelliptic equations (2008)
  • Author(s): Norio Yoshida
  • Organizer: The Fifth World Congress of NonlinearAnalysts
  • Place of Presentation: Hyatt Grand Cypress Resort, Orlando,Florida, USA.
  • Year and Date: 2008-07-03
• [Presentation] Sturmian comparison and oscillation theorems for a class of half-linear elliptic equations (2008)
  • Author(s): Norio Yoshida
  • Organizer: The Fifth World Congress of Nonlinear Analysts
  • Place of Presentation: Hyatt Grand Cypress Resort, Orlando, Florida, USA.
  • Year and Date: 2008-07-03
• [Presentation] Sturmian comparison and oscillation theorems for a class of half-linear elliptic equations (2008)
  • Author(s): Norio Yoshida
  • Organizer: Fifth World Congress of Nonlinear Analysts
  • Place of Presentation: Orlando, USA
  • Year and Date: 2008-07-03
• [Presentation] Picone identities and oscillation theory for quasilinear elliptic equations with p(x)-Laplacians
  • Author(s): Norio Yoshida
  • Organizer: 6th World Congress of Nonlinear Analysts
  • Place of Presentation: University of Athens, Greece
• [Presentation] Picone identities for half-linear elliptic equations with p(x)-Laplacians and applications
  • Author(s): 吉田範夫
  • Organizer: RIMS 共同研究「異常拡散の数理」
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] Vibrations of Timoshenko beams with damping and forcing terms
  • Author(s): Norio Yoshida
  • Organizer: The IEEE International Conference on Industrial Engineering and Engineering Management
  • Place of Presentation: Hong Kong, P.R. China
• [Book] Oscillation Theory of Partial Differential Equations (2008)
  • Author(s): Norio Yoshida
  • Publisher: World Scientific Publishing Co. Pte. Ltd.
• [Book] Oscillation Theory of Partial Differential Equations (2008)
  • Author(s): Norio Yoshida
  • Publisher: World Scientific Publishing Co. Pte.Ltd.
• [Book] Oscillation Theory of Partial Differential Equations (2008)
  • Author(s): Norio Yoshida
  • Total Pages: 326
  • Publisher: World Scientific Publishing Co. Ltd.