Research Article

Monotone ODEs with discontinuous vector fields in sequence spaces

Published in: Quaestiones Mathematicae
Volume 46 , issue 12 , 2023 , pages: 2701–2718

DOI: 10.2989/16073606.2023.2182242

Author(s): Oleg Zubelevich Steklov Mathematical Institute of Russian Academy of Sciences, Russia

Keywords: 58D25 , 46A04 , 46A45 , 47H07 , 47J35 , 34G20 , Infinite-dimensional evolution equations , infinite-order system of ODEs , countable system of ODEs

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Abstract

We consider a system of ODE in a Fréchet space with unconditional Schauder basis. The right side of the ODE is a discontinuous function. Under certain monotonicity conditions we prove an existence theorem for the corresponding initial value problem. We employ an idea of the partial order which seems to be new in this field.

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