臺灣博碩士論文加值系統

我們研究p-拉普拉斯問題正解的分支曲線
{█((φ_p (u'(x)))'+λf(u)=0,-1<x<1,@u(-1)=u(1)=0,)┤
在這裡 p>1,φ_p (y)=|y|^(p-2) y,(φ_p (u'(x)))' 是一維的p-拉普拉斯，λ > 0是一個分支參數而非線性四次多項式f(u)=－u^(p+2)+σu^(p+1)-τu^p+ρu^(p-1)恰有三個正實根且σ, τ ∈ ℝ, ρ ≥ 0。則我們在 (λ‚‖u‖_∞ )平面上研究分支曲線的圖形，因此我們能夠用σ, τ, ρ和 λ的值來確定正解的個數。

We study bifurcation curves of positive solutions for the p-Laplacian problem
{█((φ_p (u'(x)))'+λf(u)=0,-1<x<1,@u(-1)=u(1)=0,)┤
where p>1,φ_p (y)=|y|^(p-2) y,(φ_p (u'(x)))' is the one-dimensional p-Laplacian, λ > 0 is a bifurcation parameter, and the nonlinearity f(u)=－u^(p+2)+σu^(p+1)-τu^p+ρu^(p-1) with σ, τ ∈ ℝ, ρ ≥ 0 has exactly three positive zeros. Then on the (λ‚‖u‖_∞ )-plane, we study shapes of bifurcation curves, and hence we are able to determine the multiplicity of positive solutions by the values of σ, τ, ρ and λ.

中文摘要 i
英文摘要 ii
誌 謝 iii
目 錄 iv
1 Introduction 1
2 Main results 4
3 Lemmas 12
4 Proof of Main results 22
Reference 30

References
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