The Oscillation Properties Of The Boundary Value Problem With Spectral Parameter In The Boundary Condition

The spectral problem is investigated for the fourth order ordinary differential operator with spectral parameter in the boundary conditions. The oscillation properties of the eigenfunctions of this problem are established

Spectral Properties of the Differential Operators of the Fourth-Order with Eigenvalue Parameter Dependent Boundary Condition

We consider the fourth-order spectral problem y4 x−qxy x λyx, x ∈ 0, l with spectral parameter in the boundary condition. We associate this problem with a selfadjoint operator in Hilbert or Pontryagin space. Using this operator-theoretic formulation and analytic methods, we investigate locations in complex plane and multiplicities of the eigenvalues, the oscillation properties of the eigenfunctions, the basis properties in Lp0, l, p ∈ 1, ∞, of the system of root functions of this problem

Bifurcation from zero or infinity in nonlinearizable Sturm-Liouville problems with indefinite weight

In this paper, we consider bifurcation from zero or infinity of nontrivial solutions of the nonlinear Sturm–Liouville problem with indefinite weight. This problem is mainly important because of it is related with a selection-migration model in genetic population. We show the existence of four families of unbounded continua of nontrivial solutions to this problem bifurcating from intervals of the line of trivial solutions or the line R × {∞} (these intervals are called bifurcation intervals). Moreover, these global continua have the usual nodal properties in some neighborhoods of bifurcation intervals

On oscillation properties of the eigenfunctions of a fourth order differential operator

The spectral problem for a fourth order ordinary differential operator is investigated. The oscillation properties of the eigenfunctions and their derivatives are established

Investigation of the effects of constant darkness and light on blood serum cholesterol, insulin and glucose levels in healthy male rats

This study was designed to investigate the effects of constant darkness and light on changes of serum cholesterol, insulin and glucose levels in healthy male rats. In this study, healthy male rats (n = 30) were divided into 3 groups of tens and kept at various light/dark conditions: Control 12:12 light/dark (LD); constant darkness (DD), and constant light (LL) groups for 2 weeks. Blood samples were obtained from retro-orbital sinus before start of experiment and on the 7th and 14th days of the experimental period. The serum cholesterol and glucose levels were measured by the enzymatic method and insulin levels were measured using insulin kit by enzyme-linked immunosorbent assay (ELISA) method. The results of the study showed that the levels of serum cholesterol and glucose on the 7th and 14th days of the experimental period in DD group significantly decreased compared to the LD and LL groups (p < 0.05). On the 14th day of experiment, we observed significant decrease of serum insulin level in the constant darkness group compared with the two other groups (p < 0.05). The study showed that on the 7th and 14th days of experiment, constant light significantly increased serum glucose level without having any significant effects on serum cholesterol and insulin levels. Also, the long period of time (14 days) was found to be more effective in the serum of these metabolic parameters changes than the short period (7 days).Key words: Constant darkness, light, cholesterol, glucose, insulin, healthy male rats

Oscillation theorems for the Dirac operator with spectral parameter in the boundary condition

We consider the boundary value problem for the one-dimensional Dirac equation with spectral parameter dependent boundary condition. We give location of the eigenvalues on the real axis, study the oscillation properties of eigenvector-functions and obtain the asymptotic behavior of the eigenvalues and eigenvector-functions of this problem