On the ellipticity and solvability of an abstract second-order differential equation.
On the existence and uniqueness of solutions for an incomplete second-order abstract Cauchy problem
We prove existence and uniqueness of classical solutions for an incomplete second-order abstract Cauchy problem associated with operators which have polynomially bounded resolvent. Some examples of differential operators to which our abstract result applies are also included.
On the existence of continuous solutions of operator equations in Banach spaces
On the existence of solutions for a class of first-order differential equations.
On the explicit solution of a linear first order Cauchy problem with distributional coefficients.
On the mild solutions of higher-order differential equations in Banach spaces.
On the operator equation with unbounded operators , , and .
On the Perron problem for the exponential dichotomy of -semigroups.
On the quasiuniqueness of solutions of degenerate equations in Hilbert space.
On the question of generalized solution to algebro-differential systems.
On the regularity of abstract Cauchy problems and boundary value problems
Maximal regularity (in -sense) for abstract Cauchy problems of order one and boundary value problems of order two is studied. In general, regularity of the first problems implies regularity of the second ones; the converse is shown to hold if the underlying Banach space has the UMD property. A stronger notion of regularity, introduced by Sobolevskii, plays an important role in the proofs.
On the solvability of a fourth order operator differential equations.
On the solvability of the Lyapunov equation for nonselfadjoint differential operators of order 2m with nonlocal boundary conditions
This paper is devoted to the solvability of the Lyapunov equation A*U + UA = I, where A is a given nonselfadjoint differential operator of order 2m with nonlocal boundary conditions, A* is its adjoint, I is the identity operator and U is the selfadjoint operator to be found. We assume that the spectra of A* and -A are disjoint. Under this restriction we prove the existence and uniqueness of the solution of the Lyapunov equation in the class of bounded operators.
On the spectrum of weakly almost periodic solutions of certain abstract differential equations.
On the stability of stationary solutions of a linear integro-differential equation.
On the Stepanov almost periodic solution of a second-order infinitesimal generator differential equation.
On the structure of solutions sets of differential and integral equations in Banach spaces
On uniform exponential stability of periodic evolution operators in Banach spaces.
On well-posedness of the nonlocal boundary value problem for parabolic difference equations.
Opérateurs différentiels et courbes elliptiques