Oscillation properties for non-classical Sturm-Liouville problems with additional transmission conditions

• Published in: Mathematical modelling and analysis Vol. 26; no. 3; pp. 432 - 443
• Main Authors: Mukhtarov, Oktay Sh, Aydemir, Kadriye
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 09.09.2021
• Subjects: Boundary conditions; Boundary value problems; comparison theorems; Criteria; Dielectric properties; Eigenvectors; Intervals; Mathematical analysis; Mathematical functions; Mathematical research; Mathematics; non-classical slp’s; Ordinary differential equations; Oscillation; oscillatory solutions; Partial differential equations; Physics; transmission problems; Turkey; oscillatory solutions; comparison theorems; transmission problems; non-classical SLP’s
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2021.13216

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.