On correct solvability of one boundary value problems for the differential equations of the second order in Hilbert space

Abstract

In this work some boundary value problem for the operator-differential equations of the second order of elliptic type is investigated on a finite segment. Here sufficient conditions are specified operator coefficients of the equation, at which boundary value regularly or fredholm's solvability. The received results are applied to some boundary value for differential the equations of the second order in private derivatives of elliptic type.

On fredholm property of a periodic type boundary value problem

“…In an finite domain, boundary value problems with variable coefficients have been studied very little. We can note the works of S.S. Mirzoev with G.A.Agayeva [14,15 ], G.A.Agayeva [1,2,3].…”

On the solvability conditions of one boundary value problem for the second order differential equations with operator coefficients

“…The inequality (6) is proved. Let's prove inequality (7). For any ε > 0 from the inequality (9) it follows that…”

“…For ρ (t) = 1 , A 1 (t)A 1 , A 2 (t) = A 2 in the equation (1) with boundary conditions u (0) = u(t) = 0it has been considered in works [5,6], and ρ (t) = α, t ∈ (0 , T 0 ), ρ (t) = β for t ∈ (T 0 , ∞) in the infinite domain the problem has been considered in the papers [8][9][10][11]. The equation 1with boundary conditions u (0) = u(T ) = 0 has been investigated in the work [7].…”