Research on the existence of solutions of differential equations and their properties via functional analysis methods
| Project/Area Number |
21540214
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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 |
Global analysis
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| Research Institution | Yokohama National University |
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Principal Investigator |
SHIOJI Naoki 横浜国立大学, 工学研究院, 教授 (50215943)
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| Co-Investigator(Renkei-kenkyūsha) |
HIRANO Norimichi 横浜国立大学, 大学院環境情報研究院, 教授 (80134815)
TAMANO Kenichi 横浜国立大学, 大学院工学研究院, 教授 (90171892)
WATANABE Kohtaro 防衛大学校, 電気情報学群, 准教授 (30546057)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
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: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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)
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| Keywords | 関数方程式論 / 解析学 / 関数解析学 / 楕円型方程式 / 変分法 / 多重解 / 正値解 / 対称性 / 楕円幾何 / 双曲幾何 / 符号変化解 / 解の多重性 / Sobolevの臨界指数 / 変動指数 |
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| Research Abstract |
For elliptic problems which have Nehari manifold structures, there were some results on the numbers of their positive solutions. However, the numbers of sign-changing solutions were not studied well. By using category on the domain, we give a result on a number of sign-changing solutions. For elliptic problems which have Sobolev's critical exponent, the existence of solutions whose level are greater that the two times of the level of the limit equation were not discussed well. We gave such an argument to show the existence of the multiple solutions.
We also studied the uniqueness of positive radial solutions for elliptic equations. The uniqueness of a positive radial solution of the scalar field equation has a long history. We gave a uniqueness result which is applicable to various equations including the scalar field equation.
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Report
(6 results)
Research Products
(56 results)
