臺灣博碩士論文加值系統

我們研究 p-Laplacian 邊界爆炸值問題解存在之充分與必要條件.我們也研究分歧曲線 λ(ρ) 的漸近行為，其中ρ代表解u(x)在(0,1)的最小值。特別的是，我們探討分歧曲線 λ(ρ)在ρ=0的連續性。我們研究的結果有助於去決定對於給定的參數λ>0，p-Laplacian 邊界爆炸值問題解的個數，且我們也提供了幾個有趣的例子。

We investigate the necessary and sufficient conditions for the existence of solutions of the p-Laplacian boundary blow-up problem .We also study asymptotic behaviors of the bifurcation curve λ(ρ) , where ρ:=min{x in (0,1)}u(x). In particular, we study the continuity of λ(ρ) at ρ=0. Our results help to determine the number of solutions for any λ>0. Some interesting examples are given.

Contents
1.Introduction…………………………2
2.Main Results…………………………4
3.Lemmas…………………………………11
4.Proofs of Main Results……………18
References………………………………30

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