2018
Том 70
№ 4

# Solvability of semilinear differential equations with singularity

Rutkas A. G.

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.

English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 2, pp 262-276.

Citation Example: Rutkas A. G. Solvability of semilinear differential equations with singularity // Ukr. Mat. Zh. - 2008. - 60, № 2. - pp. 225–239.

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