Solvability of semilinear differential equations with singularity

  • A. G. Rutkas

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
Rutkas, A. G. “Solvability of Semilinear Differential Equations With Singularity”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, no. 2, Feb. 2008, pp. 225–239, https://umj.imath.kiev.ua/index.php/umj/article/view/3152.
Section
Research articles