The theory of ill-posed problems originated in an unusual way. As a rule, a new concept is a
subject in which its creator takes a keen interest. The concept of ill-posed problems was …

We propose new methods for the construction of generalized inverse operator matrices for
the operator matrices in Banach spaces. The solvability criteria and the formulas for …

We study weakly perturbed integrodifferential equations with degenerate kernel in Banach
spaces and establish conditions for the bifurcation of solutions of weakly perturbed …

Purpose The paper aims to study the constraint solutions of the periodic coupled operator
matrix equations by the biconjugate residual algorithm. The new algorithm can solve a lot of …

We consider a noncritical case for linear boundary-value problems posed for systems of
integrodifferential equations. We establish the existence conditions and the structure of …

With the use of the theory of generalized inversion of operators and integral operators, we
obtain a criterion of solvability and determine the general form of solutions of a linear …

By using the theory of generalized inversion of operators in Banach spaces, we establish
conditions for the generalized invertibility of integrodifferential operators with degenerate …

Linear operator equations with normally solvable operators in Hilbert and Banach spaces
are of significant theoretical and practical interest. Various types of equations of this kind and …

We propose methods for the construction of the operator matrices generalized inverse to (2×
2) operator matrices in Banach spaces. We obtain the condition of solvability and a formula …

We obtain bifurcation conditions for the solutions of weakly perturbed boundary-value
problems for operator equations in Banach spaces from the point $\varepsilon= 0$. A …