Necessary and sufficient conditions for the lipschitzian invertibility of nonlinear difference operators in the spacesl p (ℤ, ℝ) with 1≤p≤∞with 1≤p≤∞

Necessary and sufficient conditions for the Lipschitzian invertibility of the difference map

Generalization of the Mukhamadiev theorem on the invertibility of functional operators in the space of bounded functions

We establish necessary and sufficient conditions for the invertibility of the linear bounded operator d ^m / dt ^m + A in the space of functions bounded on ℝ. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 3, pp. 398–412, March, 2008.     

Necessary and sufficient conditions for the oscillation of solutions of nonlinear differential equations with pulse influence in a banach space

We obtain necessary and sufficient conditions for the oscillation of solutions of nonlinear second-order differential equations with pulse influence in a Banach space. Rovno Technical University, Rovno. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 1, pp. 98–109, January, 1999.     

Generalization of the Kneser theorem on zeros of solutions of the equation <Emphasis Type="Italic">y</Emphasis>″ + <Emphasis Type="Italic">p</Emphasis>(<Emphasis Type="Italic">t</Emphasis>)<Emphasis Type="Italic">y</Emphasis> = 0

We establish conditions for the oscillation of solutions of the equation y″ + p(t)Ay = 0 in a Banach space, where A is a bounded linear operator and p: ℝ+ → ℝ+ is a continuous function. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 4, pp. 571–576, April, 2007.     

Equations in Hilbert Spaces Whose Sets of Solutions are Invariant Under a Group Isomorphic to a One-Parameter Group of Unitary Operators

Ukrainian Mathematical Journal - We construct classes of equations in a Hilbert space whose sets of solutions are invariant under a group isomorphic to a one-parameter group of unitary operators....