2010 Fiscal Year Final Research Report
A study on the number of sign-changing solutions of two-point boundary value problems and its application
| Project/Area Number |
20740082
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Okayama University of Science |
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Principal Investigator |
TANAKA Satoshi Okayama University of Science, 理学部, 准教授 (90331959)
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| Project Period (FY) |
2008 – 2010
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| 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 |
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| 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.
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