| Project/Area Number |
15K04945
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical analysis
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| Research Institution | Ibaraki University |
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Principal Investigator |
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| Research Collaborator |
RAMOS QUOIRIN Humberto Universidad de Santiago de Chile
KAUFMANN Uriel Universidad Nacional de Córdoba
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 非線形楕円型境界値問題 / concave-convex型非線形性 / 非自明非負解 / 符号不定係数 / 分岐解析 / 正値性 / 優解劣解 / 変分的手法 / 非線形楕円型偏微分方程式 / concave-convex混合型非線形性 / concave型非線形性 / ループ形状連続体解集合 / concave-convex 型非線形性 / 符号不定変係数 / 分岐解 / ループ形状連続体 / 位相解析的手法 / 解析学 / 凹凸混合型非線形性 / 非線形境界条件 / 分岐正値解 / 変分法 |
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| Outline of Final Research Achievements |
We study concave-convex nonlinear elliptic boundary value problems, equipped with indefinite weights, in a smooth bounded domain of the Euclidean space, and investigate the existence of nontrivial nonnegative solutions and their properties.
On one hand, we have determined the bifurcation structure of the nontrivial nonnegative solutions set in some cases, as a parameter included varies. Especially, we have obtained a loop type component of nontrivial nonnegative solutions which bifurcates from the trivial solutions line.
On the other hand, we have provided certain sufficient conditions for the positivity of nontrivial nonnegative solutions. The strong maximum principle does work for nonlinear elliptic problems which are regular around zero solutions in the standard sense, in which class any nontrivial nonnegative solution so implies a positive solution. However, it does not work in general for concave-convex problems with indefinite weights.
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