2009 Fiscal Year Final Research Report
Oscillation Theory for Nonlinear Differential Equations and Its Applications to Elliptic Equations
| Project/Area Number |
19740074
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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 | Osaka Prefecture University |
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Principal Investigator |
YAMAOKA Naoto Osaka Prefecture University, 工学研究科, 准教授 (90433789)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 常微分方程式 / 楕円型方程式 / 振動理論 / 非線形摂動項 / 比較定理 / 相平面解析 / 時間遅れ |
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| Research Abstract |
The purpose of this research project is to study oscillation problems for ordinary differential equations and elliptic equations with p-Laplacian. The main results are as follows: (1) Oscillation and non-oscillation criteria are given for all nontrivial solutions of second-order damped nonlinear differential equations with one-dimensional p-Laplacian. (2) A sufficient condition is obtained for half-linear differential equations with delay nonlinear perturbations to have a non-oscillatory solution. (3) We establish a new comparison theorem on the oscillation of solutions of nonlinear differential equations with one-dimensional p-Laplacian. (4) We consider radial solutions of elliptic equations with p-Laplacian, and give sufficient conditions for the equations to have a positive solution.
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