Jódar, Lucas Solving a class of generalized Lyapunov operator differential equations without the exponential operator function. (English) Zbl 0711.34075 Publ. Mat., Barc. 34, No. 1, 25-35 (1990). A method for solving operator differential equations of the type \[ (*)\quad X'(t)=A+BX(t)+X(t)D,\quad X(0)=C_ 0, \] avoiding the exponential operator function, is given. Section 1 contains an algebraic result that provides a finite algebraic expression of the solution of generalized algebraic Lyapunov operator equation, under certain uniqueness hypothesis. Section 2 concerns with the resolution of problem (*). Section 3 provides an explicit solution for a class of generalized Riccati operator differential equations in terms of a solution of certain generalized Lyapunov equation associated to the problem. Reviewer: P.Talpalaru Cited in 1 Document MSC: 34G10 Linear differential equations in abstract spaces Keywords:operator differential equations; exponential operator function; algebraic Lyapunov operator equation; Riccati operator differential equations PDFBibTeX XMLCite \textit{L. Jódar}, Publ. Mat., Barc. 34, No. 1, 25--35 (1990; Zbl 0711.34075) Full Text: DOI EuDML