Solvability of semilinear differential equations with singularity

• Date: 2008
• Main Authors: Rutkas, A. G., Руткас, А. Г.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2008
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3152
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 opera...