Regular Sturm - Liouville Problems Whose Coefficients Depend Rationally on the Eigenvalue Parameter

Autor:	Hendrik S. V. de Snoo
Rok vydání:	1996
Předmět:	Singularity General Mathematics Mathematical analysis Free boundary problem Sturm–Liouville theory Mixed boundary condition Boundary value problem Mathematics::Spectral Theory Eigenvalues and eigenvectors Robin boundary condition Second derivative Mathematics
Zdroj:	Mathematische Nachrichten. 182:99-126
ISSN:	1522-2616 0025-584X
Popis:	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 x 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::da46dba926b9b18ce4b1c2501353ffc3 https://doi.org/10.1002/mana.19961820107 Zobrazit plný text záznamu Plný text