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URN etd-0122105-211845 Author Shing-Yuan Kung Author's Email Address kungsy@math.nsysu.edu.tw Statistics This thesis had been viewed 5206 times. Download 1802 times. Department Applied Mathematics Year 2004 Semester 1 Degree Master Type of Document Language English Title Density functions with extremal antiperiodic eigenvalues and related topics Date of Defense 2005-01-07 Page Count 31 Keyword Density functions eigenvalue Abstract In this thesis, we prove 2 theorems. First let ρ0 be

a minimizing (or maximizing) density function for the first

antiperiodic eigenvalue λ1' in E[h,H,M], then ρ0=hχ(a,b)+Hχ[0,π]/(a,b) (or ρ0=Hχ(a,b)+hχ[0,π]/(a,b)) a.e. Finally, we prove minλ1'=minμ1=minν1 where μ1 and ν1 are the first Dirichlet and second Neumann eigenvalues, respectively. Furthermore, we determine the jump point X0 of ρ0 and the corresponding eigenvalue λ1', assuming that ρ0 is symmetric about π/2 We derive the nonlinear equations for this jump point X0 and λ1',then use Mathematica to solve the equations numerically.Advisory Committee Tzon-Tzer Lu - chair

Chiu-Ya Lan - co-chair

W.C.Lian - co-chair

Chun-Kong Law - advisor

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etd-0122105-211845.pdf Date of Submission 2005-01-22