# Solvability of semilinear differential equations with singularity

### Abstract

Local theorems on the existence of solutions of the Cauchy problem for the singular equations of the form $$ \frac{d}{dt}(Au(t)) + Bu(t) = f(t, u)$$ in Banach spaces are proved. The conditions for the solvability depend on a type of the singularity of the sheaf $\lambda A + B$ of closed linear operators $A, B$. Examples and applications to finite-dimensional differential algebraic equations, infinite systems of differential equations, and partial differential equations of non-Kovalevskaya type are presented.
Published

25.02.2008

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 60, no. 2, Feb. 2008, pp. 225–239, https://umj.imath.kiev.ua/index.php/umj/article/view/3152.

Issue

Section

Research articles