| Project/Area Number |
16540144
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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 | University of Toyama |
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Principal Investigator |
YOSHIDA Norio University of Toyama, Mathematics, Professor (80033934)
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| Co-Investigator(Kenkyū-buntansha) |
KOBAYASHI Kusuo University of Toyama, Mathematics, Professor (70033925)
IKEDA Hideo University of Toyama, Mathematics, Professor (60115128)
FUJITA Yasuhiro University of Toyama, Mathematics, Associate Professor (10209067)
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| Project Period (FY) |
2004 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥3,870,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2005: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2004: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | differential equations / comparison theory / oscillation theory / zero / Picone identity / Picone-type inequality / 漸近的理論 / Picone 等式 / Picone 型不等式 / 振動 / 偏微分方程式 / 比較理論 |
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| Research Abstract |
Sufficient conditions for every solution to oscillate were obtained by establishing a Picone identity for half-linear elliptic equation. In the case where nonlinear term is the sum of superlinear term and sublinear term oscillation results were obtained via Picone-type inequalities. We established Sturmian comparison theorems for fourth order differential operators by deriving a Picone identity. For quasilinear elliptic equations where principal parts are more general than p-Laplacin we obtained oscillation results by establishing Picone identity for half-linear case and Picone-type inequality for the case where nonlinear term is the sum of superlinear term and sublinear term. Moreover, oscillation theorems were obtained for superlinear elliptic equations with forcing terms. Using Picone-type inequality applicable to quasilinear parabolic equations, we derived unboundedness of solutions and sufficient conditions for bounded solution to oscillate. All of above results are very significa
… More
nt because importance of Picone identity or Picone-type inequality was realized again. Sufficient conditions for solution of boundary value problems of parabolic equations with functional arguments and hyperbolic equations with functional arguments to oscillate were established by reducing to functional differential equations. We obtained sufficient conditions for every solution of second order neutral differential equations with positive and negative coefficients to oscillate. These results seem to contribute greatly to oscillation theory for partial differential equations and oscillation theory for functional differential equations with one variable. I gave lectures on international conferences "EQUADIFF 11", "Conference on Differential and Difference Equations and Applications", "Colloquium on Differential and Difference Equations", "EQUADIFF 2007" and it was very fruitful for me to be able to communicate with foreign researchers and get newest informations. Also I could participate in various workshops in Japan, and presented research results, and moreover I could do research arrangements. I believe that comparison theory and asymptotic theory for differential equations could be developed greatly. Less
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