Differential operator equations with interface conditions in modified direct sum spaces

Abstract

We investigate a new type boundary value problem consisting of a differential-operator equation, eigendependent boundary conditions, and two supplementary conditions so-called interface conditions. We give a characterisation of some spectral properties of the considered problem. Particularly, it is established such properties as isomorphism and coerciveness, discreteness of the spectrum and found asymptotic formulas for eigenvalues.

Oscillation Properties for Non-Classical Sturm-Liouville Problems With Additional Transmission Conditions

“…In this work we will extend and generalize some well-known Sturm's comparison and oscillation theorems for problems of a new type, which consist of Sturm-Liouville equation In recent years, the authors of this study and some other mathematicians have studied many other spectral properties of similar BTVP's (see, for example, [1,2,4,5,6,7,9,13,17,22,23,27,28]). BVTP's also find many important application in the study of various phenomena in physics and technology, such as vibration of string involving different types of loads (see, for example, [12,14,18,21,25,26]), heat transfer through a solid-liquid interface(see, for example, [8,15,20]), water vapor diffusion through a porous membrane (see, for example, [24]).…”

Yeni Tipten Sturm-Liouville Problemlerinin Ürettiği Diferansiyel Operatörlerin Kendine Eşlenikliği ve Pozitivliği

“…The completeness of the eigenfunctions and eigenfunction expansions in various function spaces for the Sturm-Liouville problems with spectral parameter in the boundary conditions have been considered in [10][11][12][13][14][15][16]. Problems with various singularities have been analyzed in [17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”

A Study of The Scattering Properties of Eigenparameter- Dependent Matrix Difference Operator With Transmission Condition

“…Compared to the whole process, the duration of this sudden and sharp change is negligible, but the functioning of this system still changes. These short-term effects are called impulse effects, and to deal with these effects, the conditions called transmission condition, point interaction, impulsive condition, jump condition and interface condition are applied to the value problem [1,21,26,28,29]. Non-stationary biological systems such as heart rhythm beats, blood flows, population dynamics; physical phenomena with variable structure such as theoretical physics, atomic physics, radiophysics, phormacokinetics, and many other such as mathematical economy, chemical technology, electrical technology, metallurgy, ecology, industrial robotics, medicine contain impulse effects.…”