2001 Fiscal Year Annual Research Report

高階非線形微分方程式の解の零点の個数に関する研究

Research Project

Project/Area Number	13640178
Research Institution	Ehime University
Principal Investigator	内藤学愛媛大学, 理学部, 教授 (00106791)
Co-Investigator(Kenkyū-buntansha)	宇佐美広介広島大学, 総合科学部, 助教授 (90192509) 橋本貴宏愛媛大学, 理学部, 助手 (60291499) 坂口茂愛媛大学, 理学部, 教授 (50215620)
Keywords	非線形微分方程式 / 非振動解 / 正値解 / 零点 / 固有値問題
Research Abstract	本研究の目的は、Emden-Fowler型の非線形項をもつ高階常微分方程式に対して、解の零点の個数・分布を調べることである。また、常微分方程式についての結果を念頭において、高階楕円型偏微分方程式の解の振動的性質を詳しく調べることである。この研究によって得られた新しい結果、新しい知見は主として次の様なものである。 1.特別な形の高階非線形常微分方程式の非振動解で無限遠点において或る特別な漸近挙動をするものの零点の個数について考察し、高階の場合でも、部分的に、2階Sturm-Liouville線形正則固有値問題と類似の結果を得ることができることを明らかにした。 2.ある種のhalf-linear非線形2階常微分方程式の非振動解で、無限遠点でminimalとなるものの零点の個数は、パラメータとともに、丁度1個づつ変化していくことを明らかにした。 3.ある種のhalf-linear非線形2階常微分方程式の解の全体の構造を完全に決定した。 4.3階のEmden-Fowler型常微分方程式の正値解の漸近挙動を完全に解明した。 5.主要項がp-Laplacianの楕円型方程式を無限管状領域で考察し、正値解の存在・非存在の臨界指数を決定した。

Research Products
(12 results)

All Other

All Publications (12 results)

[Publications] Manabu Naito: "On the number of zeros of nonoscillatory solutions to higher-order linear ordinary differential equations"Monatshefte fur Mathematik. (To appear).
[Publications] Masatsugu Mizukami, Manabu Naito, Hiroyuki Usami: "Asymptotic behavior of solutions of a class of second order quasilinear ordinary differential equations"Hiroshima Mathematical Journal. (To appear).
[Publications] Kusano Takasi, Manabu Naito, Wu Fentao: "On the oscillation of solutions of 4-dimensional Emden-Fowler differential systems"Advances in Mathematical Sciences and Applications. 11・2. (2001)
[Publications] Takasi Kusano, Manabu Naito: "Sturm-Liouville eigenvalue problems for half-linear ordinary differential equations"Rocky Mountain Journal of Mathematics. 31・3. 1039-1054 (2001)
[Publications] R.Magnanini, Shigeru Sakaguchi: "Stationary critical points of the heart flow in the plane"Journal d'Analyse Mathematique. (To appear).
[Publications] Shigeru Sakaguchi: "Regularity of the interfaces with sign changes of solutions of the one-dimensional porous medium equation"Journal of Differential Equations. 178・1. 1-59 (2002)
[Publications] Shigeru Sakaguchi: "Stationary critical points of the heat flow in spaces of constant curvature"Journal of London Mathematical Society (2). 63・2. 400-412 (2001)
[Publications] Hashimoto Takahiro, Ishiwada Michinori, Otani Mitsuharu: "Quasilinear elliptic equations in infinite tube-shaped domains"Advances in Mathematical Sciences and Applications. 11・2(印刷中). (2001)
[Publications] Ken-ichi Kamo, Hiroyuki Usami: "Asymptotic forms of positive solutions of third-order Emden-Fowler equationns"Journal of Mathematical Analysis and Applications. (To appear).
[Publications] Tomomitsu Teramoto, Hiroyuki Usami: "A Liouville type theorem for semilinear elliptic systems"Pacific Journal of Mathematics. (To appear).
[Publications] Ken-ichi Kamo, Hiroyuki Usami: "Asymptotic forms of positive solutions of second-order quasilinear ordinary differential equations with sub-homogeneity"Hiroshima Mathematical Journal. 31・1. 35-49 (2001)
[Publications] Yuki Naito, Hiroyuki Usami: "Oscillation criteria for quasilinear elliptic equations"Nonlinear Analysis. Theory, Methods and Applications. 46・5. 629-652 (2001)

2001 Fiscal Year Annual Research Report

高階非線形微分方程式の解の零点の個数に関する研究

Principal Investigator

内藤 学 愛媛大学, 理学部, 教授 (00106791)

Research Products

[Publications] Manabu Naito: "On the number of zeros of nonoscillatory solutions to higher-order linear ordinary differential equations"Monatshefte fur Mathematik. (To appear).

[Publications] Masatsugu Mizukami, Manabu Naito, Hiroyuki Usami: "Asymptotic behavior of solutions of a class of second order quasilinear ordinary differential equations"Hiroshima Mathematical Journal. (To appear).

[Publications] Kusano Takasi, Manabu Naito, Wu Fentao: "On the oscillation of solutions of 4-dimensional Emden-Fowler differential systems"Advances in Mathematical Sciences and Applications. 11・2. (2001)

[Publications] Takasi Kusano, Manabu Naito: "Sturm-Liouville eigenvalue problems for half-linear ordinary differential equations"Rocky Mountain Journal of Mathematics. 31・3. 1039-1054 (2001)

[Publications] R.Magnanini, Shigeru Sakaguchi: "Stationary critical points of the heart flow in the plane"Journal d'Analyse Mathematique. (To appear).

[Publications] Shigeru Sakaguchi: "Regularity of the interfaces with sign changes of solutions of the one-dimensional porous medium equation"Journal of Differential Equations. 178・1. 1-59 (2002)

[Publications] Shigeru Sakaguchi: "Stationary critical points of the heat flow in spaces of constant curvature"Journal of London Mathematical Society (2). 63・2. 400-412 (2001)

[Publications] Hashimoto Takahiro, Ishiwada Michinori, Otani Mitsuharu: "Quasilinear elliptic equations in infinite tube-shaped domains"Advances in Mathematical Sciences and Applications. 11・2(印刷中). (2001)

[Publications] Ken-ichi Kamo, Hiroyuki Usami: "Asymptotic forms of positive solutions of third-order Emden-Fowler equationns"Journal of Mathematical Analysis and Applications. (To appear).

[Publications] Tomomitsu Teramoto, Hiroyuki Usami: "A Liouville type theorem for semilinear elliptic systems"Pacific Journal of Mathematics. (To appear).

[Publications] Ken-ichi Kamo, Hiroyuki Usami: "Asymptotic forms of positive solutions of second-order quasilinear ordinary differential equations with sub-homogeneity"Hiroshima Mathematical Journal. 31・1. 35-49 (2001)

[Publications] Yuki Naito, Hiroyuki Usami: "Oscillation criteria for quasilinear elliptic equations"Nonlinear Analysis. Theory, Methods and Applications. 46・5. 629-652 (2001)

内藤学愛媛大学, 理学部, 教授 (00106791)