Aslanov, Afgan2024-03-132024-03-1320090035-7596https://doi.org/10.1216/RMJ-2009-39-6-1809https://hdl.handle.net/20.500.12662/3734In this paper we give some new results concerning solvability of first order singular problems. We study mainly the differential equation x' = f(t, x). We prove that the existence theorem of Caratheodory remains true if f is not defined at the given initial point and satisfies more flexible conditions. This theorem allows us to develop theorems on the existence and uniqueness of the solution of systems of differential equations and high order differential equations. We introduce a more general form of the initial value problems and try to develop this idea.eninfo:eu-repo/semantics/openAccessInitial value problemCaratheodory's theoremsingularityArticle10.1216/RMJ-2009-39-6-18092-s2.0-7654910465018356Q2180939WOS:000273523500003Q4