Precise asymptotic analysis of solutions of nonlinear differential equations by means of regular variation: The theoretical face and back sides for oscillation theory
| Project/Area Number |
23540218
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Kumamoto University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2011-04-28 – 2016-03-31
|
| Project Status |
Completed (Fiscal Year 2015)
|
| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
|---|
| Keywords | 微分方程式論 / 振動理論 / 非振動解の漸近挙動 / 正則変動関数論 / 微分方程式 / 国際研究者交流 / 多国籍 |
|---|
| Outline of Final Research Achievements |
The purpose of this research subject is devoted to the asymptotic analysis of the nonoscillatory behavior of several types of the nonlinear differential equations. Our main results obtained are as belows.
(1) The existence and the asymptotic behavior for the large value of the variable of the positive solutions of generalized Thomas-Fermi equation are proved. (2) We establish a sharp condition of the existence of generalized regularly varying functions (in the sense of Karamata) of self-adjoint functional differential equation. (3) We devote to the asymptotic analysis of a class of the third order sublinear differential equation. (4) We demonstrate that the method of regular variation can be effectively applied to fourth order quasilinear differential equations. (5) We show that an application of the theory of regular variation gives the possibility of determining the existence and precise asymptotic behavior of positive solutions of the third order nonlinear differential equation
|
Report
(6 results)
Research Products
(35 results)
