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Bifurcation for Singular p-Laplacian Problems with Convection Term

Author: ZhangYaoXing
Tutor: ZhaoPeiHao
School: Lanzhou University
Course: Basic mathematics
Keywords: bifurcation convection term p-Laplacian
CLC: O175.8
Type: Master's thesis
Year: 2010
Downloads: 7
Quote: 0
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Abstract


In this paper,we study the bifurcation problem whereλ,μ≥0,andΩis bounded domain in RN.The singular character of the problem is given by the nonlinearity g which is assumed to be strictly decreasing and unbounded around the origin.We use the skill to eliminate the conviction term and combine the maxmium principle and the Picone’s identity for the p-Laplacian to prove that the above problem has a positive solution(which is unique)ifλ(α+μ)<λ1；it has no positive solution ifλ(α+μ)≥λ1,whereα=limt→∞g(t)andλ1 is the first eigenvalue of—Δp in W01,p(Ω).

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Boundary Value Problems
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