Premium
Regular Sturm ‐ Liouville Problems Whose Coefficients Depend Rationally on the Eigenvalue Parameter
Author(s) -
De Snoo Henk
Publication year - 1996
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19961820107
Subject(s) - mathematics , eigenvalues and eigenvectors , sturm–liouville theory , singularity , mathematical analysis , boundary (topology) , boundary value problem , function (biology) , order (exchange) , type (biology) , coefficient matrix , ecology , physics , finance , quantum mechanics , evolutionary biology , economics , biology
In this note we consider regular Sturm‐Liouville equations with a floating singularity of a special type: the coefficient of the second order derivative contains the eigenvalue parameter. We determine the form of the boundary conditions which make the problem selfadjoint after linearizing. In general the boundary conditions for the linearized system give rise to boundary conditions which involve the eigenvalue parameter in the original, non‐linearized, problem. The boundary conditions give rise to a 2 × 2 matrix function, the so‐called Titchmarsh‐Weyl coefficient. The characteristic properties of this function are studied. The formal aspects of the theory of this class of equations turn out to be quite parallel to those for the usual situation when there is no floating singularity.