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On Necessary and Sufficient Conditions for the Existence of Solutions of a P-Laplacian Boundary Blow-up Problem
Thesis

On Necessary and Sufficient Conditions for the Existence of Solutions of a P-Laplacian Boundary Blow-up Problem

Pei-yu Huang
Masters, 國立清華大學, 數學系
2001

Abstract

P次拉普拉斯算子 邊界爆炸值問題 非負解 變號解 存在 分歧曲線 多樣性 P-Laplacian Boundary Blow-up Problem nonnegative solution sign-changing solution existence multiplicity bifurcation
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.

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