### Title page for etd-0727111-224827

URN etd-0727111-224827 Wan-Zhen Wang No Public. This thesis had been viewed 5269 times. Download 1072 times. Applied Mathematics 2010 2 Master English p- Laplacian operators with L^1 coefficient functions 2011-06-10 54 p-Laplacian generalized Prufer substitution Caratheodory problem Sturm oscillation theorem Sturm-Liouville properties In this thesis, we consider the following one dimensional p-Laplacian eigenvalue problem:-((y’/s)^(p-1))’+(p-1)(q-λw)y^(p-1)=0 a.e. on (0,1)   (0.1)and satisfyαy(0)+ α ’ (y’(0)/s(0))=0 βy(1)+β’ (y’(1)/s(1))=0            (0.2)where f^(p-1)=|f|^p-2 f=|f|^p-1 sgnf; α, α’, β, β’ ∈R such that α^2+α’^2>0 andβ^2+β’^2>0;and the functions s,q,w are required to satisfy (1) s,q,w∈L^1(0,1);(2) for 0≤x≤1, we have s≥0,w≥0 a.e.;(3) for any x∈ (0,1), ∫_0^1 s(t)dt>0, ∫_0^x w(t)dt>0,and∫_x^1 w(t)dt>0;(4) if for some x_10 and ∫_ζ_2k+1^(n)^ ζ_2k+2^(n) s>0.We call the above conditions Atkinson conditions, first introduce in [1].There conditions include the case when s,q,w∈L^1(0,1) and s,w>0 a.e.We use a generalized Prufer substitution and Caratheodory theorem to prove the existence and uniqueness for the solution of the initial value problem of (0.1) above. Then we generalize the Sturm oscillation theorem to one dimensional p-Laplacian and establish the Sturm-Liouville properties of the p-Laplacian operators with L^1 coefficient functions. Our results filled up some gaps in Binding-Drabek [3]. W.C. Lian - chair Tzon-Tzer Lu - co-chair Tsung-Lin Lee - co-chair Chun-Kong Law - advisor indicate accessible in a year 2011-07-27

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