Class Of Operator-differential Equations Research Articles

Splitting Schemes for One Class of Operator Differential Equations

Splitting Schemes for One Class of Operator Differential Equations

On a Class of Operator-Differential Equations of the Third Order With Multiple Characteristics on the Whole Axis in the Weighted Space

Abstract In this paper, the conditions of correct solvability are found for a class of the third order operator-differential equations whose principal part has multiple characteristics in the Sobolev type space with exponential weight. The estimations of the norms of intermediate derivative operators closely connected with the solvability conditions are carried out. Moreover, the connection between the weight exponent and the lower bound of the spectrum of the main operator involved in the principal part of the equation is determined in the results of the paper.

On the solvability of initial boundary-value problems for a class of operator-differential equations of third order

We obtain sufficient conditions for the regular solvability of initial boundary-value problems for a class of operator-differential equations of third order with variable coefficients on the semiaxis. These conditions are expressed only in terms of the operator coefficients of the equations under study. We obtain estimates of the norms of intermediate derivative operators via the discontinuous principal parts of the equations and also find relations between these estimates and the conditions for regular solvability.

Completeness of a system of elementary solutions to a class of operator-differential equations on a finite interval

Completeness of a system of elementary solutions to a class of operator-differential equations on a finite interval

On the boundary-value problem for a class of operator-differential equations of third order

On the boundary-value problem for a class of operator-differential equations of third order

On the Correct Solvability of the Boundary-Value Problem for One Class Operator-Differential Equations of the Fourth Order with Complex Characteristics

Sufficient coefficient conditions for the correct and unique solvability of the boundary-value problem for one class of operator-differential equations of the fourth order with complex characteristics, which cover the equations arising in solving the problems of stability of plastic plates, are obtained in this paper. Exact values of the norms of operators of intermediate derivatives, which are involved in the perturbed part of the operator-differential equation under investigation, are found along with these in subspaces in relation to the norms of the operator generated by the main part of this equation. It is noted that this problem has its own mathematical interest.

On the boundary value problem for a class of operator-differential equations of odd order with variable coefficients

where A 1 ( t ), A 2 ( t ), …, A 4 k – 1 ( t ) are linear generally unbounded operators determined for almost all t ∈ � + ; A is a self-adjoint positive definite operator on a separable Hilbert space H , ρ ( t ) = α for 0 ≤ t ≤ T and ρ ( t ) = β for T < t < + ∞ , where α and β are positive generally unequal numbers; f ( t ) ∈ L 2 ( � + ; H ) ; u ( t ) ∈ ( � + ; H ) (see [1]); and u ( j ) ≡ is a derivative in the sense of distributions.

Boundary-Value Problems for a Class of Operator Differential Equations of High Order with Variable Coefficients

In this paper, we obtain sufficient conditions for the existence of a unique regular solution of the boundary-value problems for operator differential equations of order 2k with variable coefficients. These conditions are expressed solely in terms of operator coefficients of the equations under study.

Elements of nonstationary scattering theory for a class of operator-differential equations

Elements of nonstationary scattering theory for a class of operator-differential equations

Cauchy problems for a certain class of operator differential equations with nonsmooth periodic coefficients

In a Hilbert space one considers the differential equation with completely continuous operator F and a nonsmooth periodic operator coefficient L(t) that is close to a positive-definite operator. One constructs a complete collection of operator solutions of the investigated equation.