Exact Multiplicity of Positive Solution for a p-Laplacian Problem Involving a Nonlinearity with Exactly One Positive Zero

Exact Multiplicity of Positive Solution for a p-Laplacian Problem Involving a Nonlinearity with Exactly One Positive Zero

碩士 === 國立臺南大學 === 應用數學系碩士班 === 104 === We study bifurcation curves of positive solutions for a 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 n...

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Main Authors: YEH,CHIEH, 葉杰
Other Authors: YEH,TZUNG-SHIN
Format: Others
Language:en_US
Published: 2016
Online Access:http://ndltd.ncl.edu.tw/handle/63150887917268912821
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spelling ndltd-TW-104NTNT05070112017-09-03T04:25:15Z http://ndltd.ncl.edu.tw/handle/63150887917268912821 Exact Multiplicity of Positive Solution for a p-Laplacian Problem Involving a Nonlinearity with Exactly One Positive Zero 包含恰有一個正零根的非線性函數p-拉普拉斯問題正解的確切個數 YEH,CHIEH 葉杰 碩士 國立臺南大學 應用數學系碩士班 104 We study bifurcation curves of positive solutions for a 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} has exactly one positive simple zero, σ,τ∈ℝ, ρ≥0. Then on the (λ,||u||∞)-plane, we give a classification of three qualitatively different bifurcation curves: an S-shaped curve, a ⊂-shaped curve and a monotone increasing curve. YEH,TZUNG-SHIN 葉宗鑫 2016 學位論文 ; thesis 24 en_US
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language en_US
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sources NDLTD
description 碩士 === 國立臺南大學 === 應用數學系碩士班 === 104 === We study bifurcation curves of positive solutions for a 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} has exactly one positive simple zero, σ,τ∈ℝ, ρ≥0. Then on the (λ,||u||∞)-plane, we give a classification of three qualitatively different bifurcation curves: an S-shaped curve, a ⊂-shaped curve and a monotone increasing curve.
author2 YEH,TZUNG-SHIN
author_facet YEH,TZUNG-SHIN
YEH,CHIEH
葉杰
author YEH,CHIEH
葉杰
spellingShingle YEH,CHIEH
葉杰
Exact Multiplicity of Positive Solution for a p-Laplacian Problem Involving a Nonlinearity with Exactly One Positive Zero
author_sort YEH,CHIEH
title Exact Multiplicity of Positive Solution for a p-Laplacian Problem Involving a Nonlinearity with Exactly One Positive Zero
title_short Exact Multiplicity of Positive Solution for a p-Laplacian Problem Involving a Nonlinearity with Exactly One Positive Zero
title_full Exact Multiplicity of Positive Solution for a p-Laplacian Problem Involving a Nonlinearity with Exactly One Positive Zero
title_fullStr Exact Multiplicity of Positive Solution for a p-Laplacian Problem Involving a Nonlinearity with Exactly One Positive Zero
title_full_unstemmed Exact Multiplicity of Positive Solution for a p-Laplacian Problem Involving a Nonlinearity with Exactly One Positive Zero
title_sort exact multiplicity of positive solution for a p-laplacian problem involving a nonlinearity with exactly one positive zero
publishDate 2016
url http://ndltd.ncl.edu.tw/handle/63150887917268912821
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