A study on the number of sign-changing solutions of two-point boundary value problems and its application

• Project/Area Number: 20740082
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Okayama University of Science
• Principal Investigator: TANAKA Satoshi Okayama University of Science, 理学部, 准教授 (90331959)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000); Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: 2点境界値問題 / 符号変化する解 / 球対称解 / Emden-Fowler型方程式 / 一意性 / 正値解 / Henon方程式 / 符号の変化する解

Research Abstract

In this study, two-point boundary value problems for nonlinear ordinary differential equations are considered. New results for the uniqueness of sign-changing solutions are established. As its application we have obtained sufficient conditions for the uniqueness of sign-changing radial solutions of boundary value problems of elliptic partial differential equations in a ball. Moreover the nonuniqueness examples for sign-changing radial solutions are also given. It is expected that we can obtain exact multiplicity results for sign-changing solutions of two-point boundary value problems by applying the method used here.

Research Products

• [Journal Article] Eventually positive solutions of first order nonlinear differential equations with a deviating argument (2010)
  • Author(s): Taizou Sakamoto, Satoshi Tanaka
  • Journal Title: Acta Mathematica Hungarica 127巻 Pages: 17-33
  • Peer Reviewed
• [Journal Article] On the uniqueness of positive solutions for two-point boundary value problems of Emden-Fowler differential equations (2010)
  • Author(s): Satoshi Tanaka
  • Journal Title: Mathematica Bohemica 135巻 Pages: 189-198
  • Peer Reviewed
• [Journal Article] On the uniqueness of positive solutions for two-point boundary value problems of Emden-Fowler differential equations (2010)
  • Author(s): Satoshi Tanaka
  • Journal Title: Mathematica Bohemica Volume: 135 Pages: 189-198
  • Peer Reviewed
• [Journal Article] Eventually positive solutions of first order nonlinear differential equations with a deviating argument (2010)
  • Author(s): Taizo Sakamoto, Satoshi Tanaka
  • Journal Title: Acta Mathematica Hungarica Volume: 127 Pages: 17-33
  • Peer Reviewed
• [Journal Article] Uniqueness and nonuniqueness of nodal radial solutions of sublinear elliptic equations in a ball (2009)
  • Author(s): Satoshi Tanaka
  • Journal Title: Nonlinear Analysis 71巻 Pages: 5256-5267
  • Peer Reviewed
• [Journal Article] Uniqueness and nonuniqueness of nodal radial solutions of sublinear elliptic equations in a ball (2009)
  • Author(s): Satoshi Tanaka
  • Journal Title: Nonlinear Analysis 71 Pages: 5256-5267
  • Peer Reviewed
• [Journal Article] Uniqueness of nodal radial solutions superlinear elliptic equations in a ball (2008)
  • Author(s): Satoshi Tanaka
  • Journal Title: Proceedings of the Royal Society of Edinburgh : Section A Mathematics 138巻 Pages: 1331-1343
  • Peer Reviewed
• [Journal Article] An identity for a quasilinear ODE and its applications to the uniqueness of solutions of BVPs (2008)
  • Author(s): Satoshi Tanaka
  • Journal Title: Journal of Mathematical Analysis and Applications 351巻 Pages: 206-217
  • Peer Reviewed
• [Journal Article] Uniqueness of nodal radial solutions superlinear elliptic equations in a ball (2008)
  • Author(s): Satoshi Tanaka
  • Journal Title: Proceedings of the Royal Society of Edinburgh : Section A Mathematics 138 Pages: 1331-1343
  • Peer Reviewed
• [Journal Article] An identity for a quasilinear ODE and its applications to the uniqueness of solutions of BVPs (2008)
  • Author(s): Satoshi Tanaka
  • Journal Title: Journal of Mathematical Analysis and Applications 351 Pages: 206-217
  • Peer Reviewed
• [Journal Article] Rectifiable oscillations of self-adjoint and damped linear differential equations of second-order
  • Author(s): Mervan Pasic, Satoshi Tanaka
  • Journal Title: Journal of Mathematical Analysis and Applications 掲載決定
  • Peer Reviewed
• [Presentation] On the nonuniqueness of positive solutions of boundary value problems for superlinear Emden-Fowler equations (2010)
  • Author(s): 田中敏
  • Organizer: RIMS 研究集会新しい視点からの現象解析と関数方程式
  • Place of Presentation: 京都大学
  • Year and Date: 2010-11-12
• [Presentation] On the nonuniqueness of positive solutions of boundary value problems for superlinear Emden-Fowler equations (2010)
  • Author(s): Satoshi Tanaka
  • Organizer: RIMS研究集会新しい視点からの現象解析と関数方程式
  • Place of Presentation: 京都大学 数理解析研究所
  • Year and Date: 2010-11-12
• [Presentation] Uniqueness of positive radial solutions of superlinear elliptic equations in a ball (2010)
  • Author(s): Satoshi Tanaka
  • Organizer: 8th AIMS International Conference on Dynamic Systems and Differential Equations
  • Place of Presentation: ドイツドレスデン
  • Year and Date: 2010-05-27
• [Presentation] Emden-Fowler型微分方程式の2点境界値問題の正値解の一意性について (2010)
  • Author(s): 田中敏
  • Organizer: 日本数学会2009年度年会
  • Place of Presentation: 横浜市慶応大学
  • Year and Date: 2010-03-24
• [Presentation] Uniqueness and nonuniqueness of positive solutions for two-point boundary value problems of Emden-Fowler equations (2010)
  • Author(s): Satoshi Tanaka
  • Organizer: Japan-Korea Joint Workshop on Dynamical Systems and Related Topics
  • Place of Presentation: 韓国プサン
  • Year and Date: 2010-03-03
• [Presentation] On the uniqueness of positive solutions of two-point BVPs of Emden-Fowler equations (2009)
  • Author(s): Satoshi Tanaka
  • Organizer: Second Chile-Japan Workshop on Nonlinear Elliptic and Parabolic PDE
  • Place of Presentation: 東京明治大学
  • Year and Date: 2009-12-02
• [Presentation] New sufficient conditions for the uniqueness of positive solutions of boundary value problems of Emden-Fowler equations (2009)
  • Author(s): Satoshi Tanaka
  • Organizer: Interenational Workshop on Qualitative Theory of ODEs in Hiroshima 2009
  • Place of Presentation: 広島大学
  • Year and Date: 2009-11-16
• [Presentation] On the uniqueness of positive solutions for two-point boundary value problems of Emden-Fowler differential equations (2009)
  • Author(s): Satoshi Tanaka
  • Organizer: Equadiff 12
  • Place of Presentation: チェコブルノ
  • Year and Date: 2009-07-23
• [Presentation] Uniqueness of positive solutions for two-point boundary value problems of Emden-Fowler differential equations (2009)
  • Author(s): Satoshi Tanaka
  • Organizer: International Workshop on Nonlinear PDE and Applications
  • Place of Presentation: 韓国プサン
  • Year and Date: 2009-07-01
• [Presentation] Uniqueness of positive solutions for two-point boundary value problems of Emden-Fowler differential equations (2009)
  • Author(s): Satoshi Tanaka
  • Organizer: International Workshop on Nonlinear PDE and Applications
  • Place of Presentation: 韓国 釜山大学
  • Year and Date: 2009-07-01
• [Presentation] On the nonuniqueness of nodal radial solutions of sublinear elliptic equations in a ball (2009)
  • Author(s): 田中敏
  • Organizer: 日本数学会2008年度年会
  • Place of Presentation: 東京大学
  • Year and Date: 2009-03-26
• [Presentation] Uniqueness and nonuniqueness of nodal radial solutions of sublinear elliptic equations in a bal (2008)
  • Author(s): 田中敏
  • Organizer: 非線形偏微分方程式における定常問題
  • Place of Presentation: 神戸大学
  • Year and Date: 2008-12-10
• [Presentation] An identity for BVPs with the one-dimensional p-Laplacian and its applications to the uniqueness of solutions (2008)
  • Author(s): Satoshi Tanaka
  • Organizer: Intensive Lecture Program and International Conference on Nonlinear PDE and Applications
  • Place of Presentation: 韓国プサン
  • Year and Date: 2008-06-13
• [Presentation] On the uniqueness of nodal radial solutions of sublinear elliptic equations in a ball (2008)
  • Author(s): Satoshi Tanaka
  • Organizer: 7th AIMS International Conference on Dyn.Systems, Diff.Equations and Applications
  • Place of Presentation: アメリカテキサスアーリントン
  • Year and Date: 2008-05-21
• [Remarks] ホームページ等
  • URL: http://www.xmath.ous.ac.jp/~tanaka/