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

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.

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.

Cite this paper

Pokutnyi, O. (2015) Boundary Value Problem for an Operator-Differential Riccati Equation in the Hilbert Space on the Interval.*Advances in Pure Mathematics*, **5**, 865-873. doi: 10.4236/apm.2015.514081.

Pokutnyi, O. (2015) Boundary Value Problem for an Operator-Differential Riccati Equation in the Hilbert Space on the Interval.

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