2014/10/23 by Rodrigo Meneses Pacheco, Pacheco, Rodrigo Meneses, Oscar Orellana +1
Computer Science · Mathematics · #34B24 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Spectral Theory in Mathematical Physics #math.CA #msc:34B24
paper · pdf · doi:10.48550/arxiv.1410.6235
arxiv created 2014/10/23 · openalex publication_date 2014/10/23 · arxiv updated 2014/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a complete description on the spectrum and eigenfunctions of the following two point boundary value problem (p(x)f')'-(q(x)-λr(x))f=0 , 0<x<L ; f'(0)=(α1 λ+ α2) f(0) ; f'(L)=(β1λ-β2)f(L), where λ and αi, βi are spectral and physical parameters. Our survey is focused mainly in the case α1>0 and β1<0, where neither self adjoint operator theorems on Hilbert spaces nor Sturm's comparison results can be used directly. We describe the spectrum and the oscillatory results of the eigenfunctions from a geometrical approach, using a function related to the Prüfer angle. The proofs of the asymptotic results of the eigenvalues and separation theorem of the eigenfunctions are developed through classical second order differential equation tools. Finally, the results on the spectrum of the equation are used for the study of the linear instability of a simple model for the fingering phenomenon on the flooding oil recovery process.