Spectral analysis for one class of second-order indefinite non-self-adjoint differential operator pencil

Oscillation Results for Second Order Self-adjoint Matrix Differential Systems

on [0,∞), where Y (t), P (t) and Q(t) are n × n real continuous matrix functions on [0,∞) with P (t), Q(t) symmetric and P (t) positive definite for t ∈ [0,∞) (P (t) > 0, t ≥ 0). A solution Y (t) of (1.1) is said to be nontrivial if det Y (t) 6= 0 for at least one t ∈ [0,∞) and a nontrivial solution Y (t) of (1.1) is said to be prepared (selfconjugated) if Y ∗(t)P (t)Y ′(t)− Y ∗′(t)P (t)Y (t) ≡...

Spectral Behaviour of a Simple Non-self-adjoint Operator

We investigate the spectrum of a typical non-selfadjoint differential operator AD = −d2/dx2 ⊗ A acting on L(0, 1) ⊗ C, where A is a 2 × 2 constant matrix. We impose Dirichlet and Neumann boundary conditions in the first and second coordinate respectively at both ends of [0, 1] ⊂ R. For A ∈ R we explore in detail the connection between the entries of A and the spectrum of AD, we find necessary c...

Behavior of Solutions of Second Order Self- Adjoint Differential Equations

On Self-Adjoint Differential Equations of Second Order.

CRITICALITY OF ONE TERM 2n-ORDER SELF-ADJOINT DIFFERENTIAL EQUATIONS

where r(x) > 0, x ∈ R, and r ∈ Lloc(R). Eq. (1.1) appears as a base for perturbations in the oscillation theory, i.e., the studied equations are regarded as perturbations of Eq. (1.1). It is shown that certain properties of Eq. (1.1) are preserved or lost by perturbations. Therefore, it is useful to know as much as possible about Eq. (1.1) (to analyse its properties), see, e.g., [1, 3, 4, 5, 6,...