Global solvability of one degenerate semilinear differential operator equation

F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow (1966).

S. L. Campbell, Singular Systems of Differential Equations, Pitman (1980).

R. Marz, “On linear differential-algebraic equations and linearizations,” Appl. Numer. Math., 1, 279–292 (1994).

A. M. Samoilenko, M. I. Shkil’, and V. P. Yakovets’, Linear Systems of Differential Equations with Degeneracies [in Ukrainian], Vyshcha Shkola, Kiev (2000).

A. G. Rutkas, “Cauchy problem for the equation $$A\frac{{dx}}{{dt}} + Bx\left( t \right) = f\left( t \right)$$ ,” Differents. Uravn., 11, No.11, 1996–2010 (1975).

A. Favini and P. Plazzi, “Some results concerning the abstract nonlinear equation D t Mu(t) + Lu(t) = f(t, Ku(t)),” in: Circuits, Systems, Signal Proc. (1986), pp. 261–274.

A. Rutkas, “The solvability of a nonlinear differential equation in a Banach space,” in: Proceedings of the Sixth Crimean Fall Mathematical School-Symposium “Spectral and Evolutionary Problems,” Simferopol (1996), pp. 317–320.

A. Favini and A. Rutkas, “Existence and uniqueness of solution of some abstract degenerate nonlinear equation,” Different. Integr. Equat., 4, No.12, 373–394 (1999).

A. G. Rutkas and L. A. Vlasenko, “Existence of solutions of degenerate nonlinear differential operator equations,” Nonlin. Oscillations, 4, No.2, 252–263 (2001).

L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces [in Russian], Fizmatgiz, Moscow (1959).

N. I. Radbel’, “On the initial manifold and dissipativity of the Cauchy problem for the equation Ax′(t) + Bx(t) = 0,” Differents. Uravn., 15, No.6 (1979).

Yu. M. Daletskii and M. G. Krein, Stability of Solutions of Differential Equations in a Banach Space [in Russian], Nauka, Moscow (1970).

V. G. Samoilenko and Yu. I. Kaplun, “Equation g(t, x) = 0: existence and extendability of its solutions,” Ukr. Mat. Zh., 53, No.3, 372–382 (2001).

I. G. Khudoshin, “Initial-value problem for some quasilinear differential-algebraic equations,” Visn. Kharkiv Univ., Ser. Mat., Prikl. Mat. Mekh., No. 458, 159–164 (1999).