2000 Fiscal Year Final Research Report Summary
Oscillatory properties of solutions of higher order differential equations
| Project/Area Number |
11640170
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | EHIME UNIVERSITY |
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Principal Investigator |
NAITO Manabu Ehime University, Faculty of Science, Professor, 理学部, 教授 (00106791)
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| Co-Investigator(Kenkyū-buntansha) |
USAMI Hiroyuki Hiroshima University, Faculty of Integrated Arts and Sciences, Associate Professor, 総合科学部, 助教授 (90192509)
HASHIMOTO Takahiro Ehime University, Faculty of Science, Assistant, 理学部, 助手 (60291499)
SAKAGUCHI Shigeru Ehime University, Faculty of Science, Associate Professor, 理学部, 助教授 (50215620)
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| Project Period (FY) |
1999 – 2000
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| Keywords | oscillation / positive solution / half-linear / eigenvalue problem / singular boundary value problem |
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| Research Abstract |
The aim of this research is to investigate the oscillatory properties of solutions of higher-order (including second-order) ordinary differential equations of the Emden-Fowler type, and to investigate the oscillatory properties of solutions of elliptic differential equations on the base of the results for ordinary differential equations.
The new results and knowledge obtained in the two years are as follows :
1. For the second-order half-linear ordinary differential equations, a generalization and an analogue of the Sturm-Liouville linear regular eigenvalue problem are obtained.
2. For the four-dimensional Emden-Fowler differential systems, a complete characterization for the existence of nonoscillatory solutions with specific asymptotic properties as t→∞ is established, and a characterization for the nonexistence of nonoscillatory solutions is also obtained.
3. For higher-order ordinary differential equations with general nonlinearities, a characterization for the existence of nonoscillatory solutions of the Kiguradze classes is established.
4. For a singular eigenvalue value problem to higher-order linear ordinary differential equations, it is shown that there is a countable sequence of eigenvalues and that the n-th eigenfunction has exactly n zeros in an infinite interval under consideration.
5. For the second-order quasilinear ordinary differential equations, the asymptotic forms of positive solutions are completely determined.
6. For the second-order quasilinear elliptic differential equations, a sufficient condition for the oscillation of all solutions is established.
7. For the two-dimensional semilinear elliptic differential systems of the Laplace type, an analogue of the Liouville theorem is established.
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Research Products
(28 results)
