Ordinary differential equations in algebras of generalized functions

Abstract

A local existence and uniqueness theorem for ODEs in the special algebra of generalized functions is established, as well as versions including parameters and dependence on initial values in the generalized sense. Finally, a Frobenius theorem is proved. In all these results, composition of generalized functions is based on the notion of c-boundedness.

LaTeX, 18 pages. An earlier version was presented at the 8th ISAAC Congress in Moscow, August 22 - 27, 2011. in S. Molahajloo, S. Pilipović, J. Toft, M.W. Wong (eds.): Pseudo-Differential Operators, Generalized Functions and Asymptotics. Operator Theory: Advances and Applications, vol. 231, pp. 253--270, Birkhäuser, Basel 2013