Solvability of semilinear differential equations with singularity

  • A. G. Rutkas


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.
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,
Research articles