On the eigenvalue problem for elliptic operator with variable coefficients and integral boundary conditions

Abstract

The talk deals with further development of the structure of spectrum for two-dimensional operator with integral conditions: [...]. Note, that in the case of p₁ = p₂ = α = β = 1, the spectrum of this operator consists only of positive eigenvalues under the condition – ∞ < γ₁ + γ₂ < γ₀ ~ 3.42. Our objective is to investigate some cases for the functions p₁, p₂, α, β and to estimate, in which cases it is possible to increase number γ₀. These results are obtained generalizing our former investigations in the case of one-dimentional eigenvalue problem [1]. Newly obtained results of the investigation of the structure of spectrum we apply for the solution of the systems of di erence equations by iterative methods. Similar results were obtained in [2].