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Krein, M.G. (1970) Stability of Solutions of Differential Equations in Banach Space. Science, Moscow, 534 p. (In Russian)

has been cited by the following article:

• TITLE: Boundary Value Problem for an Operator-Differential Riccati Equation in the Hilbert Space on the Interval

  AUTHORS: O. O. Pokutnyi

  KEYWORDS: Riccati Equation, Hamiltonian System, Generalized Green’s Operator

  JOURNAL NAME: Advances in Pure Mathematics, Vol.5 No.14, December 30, 2015

  ABSTRACT: The paper is devoted to obtaining the necessary and sufficient conditions of the solvability of weakly perturbed boundary-value problems for the nonlinear operator-differential Riccati equation in the Hilbert space on the interval and whole line with parameter ?. We find the solution of the given boundary value problem which for ε = 0 turns in one of the solutions of generating boundary value problem. Solution of the generating problem is constructed with the using generalized operator in analytical form. Iterative process for finding of solutions of weakly nonlinear equation with quadratic error is constructed.