Sturm-Liouville oscillation theory for impulsive problems

Autor:	Yu. V. Pokornyi, M. B. Zvereva, S. A. Shabrov
Rok vydání:	2008
Předmět:	Oscillation theory Distribution (number theory) General Mathematics Ordinary differential equation Mathematical analysis Riemann–Stieltjes integral Sturm–Liouville theory Gravitational singularity Absolute continuity Eigenfunction Mathematics
Zdroj:	Russian Mathematical Surveys. 63:109-153
ISSN:	1468-4829 0036-0279
DOI:	10.1070/rm2008v063n01abeh004502
Popis:	This paper extends the Sturm-Liouville oscillation theory on the distribution of zeros of eigenfunctions to the case of problems with strong singularities of the coefficients (of -function type). For instance, these are problems arising in the study of eigenoscillations of an elastic continuum with concentrated masses and localized interactions with the surrounding medium. The extension of the standard description of the problem is carried out by replacing the usual form of the ordinary differential equation by the substantially more general form with absolutely continuous solutions whose derivatives, as well as the coefficients , , , belong to . The integral is understood in the Stieltjes sense.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::7b1b8b12cb0001a50459479fb72f2354 https://doi.org/10.1070/rm2008v063n01abeh004502 Zobrazit plný text záznamu