- Turkish Journal of Mathematics and Computer Science
- Vol: 10 Special Issue
- Comparison Theorems for One Sturm-Liouville Problem with Nonlocal Boundary Conditions
Comparison Theorems for One Sturm-Liouville Problem with Nonlocal Boundary Conditions
Authors : Kadriye AYDEMİR, Hayati OLĞAR, Oktay MUKHTAROV
Pages : 121-125
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Publication Date : 2018-12-29
Article Type : Other
Abstract :n this study we present a new approach for investigation of some Sturm-Liouville systems with nonlocal boundary conditions. In the theory of boundary value problems for two-order differential equations the basic concepts and methods have been formulated studying the problems of classical mathematical physics. However, many modern problems, which arise as the mathematical modeling of some systems and processes in the fields of physics, such as the vibration of strings, the interaction of atomic particles motivate to formulate and investigate the new ones, for example, a class of Sturm-Liouville problems with nonlocal boundary conditions. Such conditions arise when we cannot measure data directly at the boundary. In this case, the problem is formulated, where the value of the solution and its derivative is linked to interior points of the considered interval. Sturm-Liouville problems together with transmission conditions at some interior points is very important for solving many problems of mathematical physics. In this study we present a new approach for investigation of boundary value problems consisting of the two interval Sturm-Liouville equations. This kind of boundary value transmission problems are connected with various physical transfer problems (for example, heat and mass transfer problems). We define a new Hilbert space and linear differential operator in it such a way that the considered nonlocal problem can be interpreted as an spectral problem. We investigate the main spectral properties of the problem under consideration. Particularly we present a new criteria for Sturm-Comparison theorems. Our main result generalizes the classical comparison theorem for regular Sturm-Liouville problems.Keywords : Boundary value problems, Comparison theorems, Transmission conditions