Open AccessOSCILLATION PROPERTIES FOR NON-CLASSICAL STURM-LIOUVILLE PROBLEMS WITH ADDITIONAL TRANSMISSION CONDITIONS
Author(s) -
O. Sh. Mukhtarov,
Kadriye Aydemir
Publication year - 2021
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/mma.2021.13216
Subject(s) - eigenfunction , oscillation (cell signaling) , mathematics , sturm–liouville theory , disjoint sets , type (biology) , boundary value problem , oscillation theory , transmission (telecommunications) , mathematical analysis , eigenvalues and eigenvectors , computer science , differential equation , physics , method of characteristics , quantum mechanics , ecology , telecommunications , genetics , exact differential equation , biology
This work is aimed at studying some comparison and oscillation properties of boundary value problems (BVP’s) of a new type, which differ from classical problems in that they are defined on two disjoint intervals and include additional transfer conditions that describe the interaction between the left and right intervals. This type of problems we call boundary value-transmission problems (BVTP’s). The main difficulty arises when studying the distribution of zeros of eigenfunctions, since it is unclear how to apply the classical methods of Sturm’s theory to problems of this type. We established new criteria for comparison and oscillation properties and new approaches used to obtain these criteria. The obtained results extend and generalizes the Sturm’s classical theorems on comparison and oscillation.