Monotone ODEs with Discontinuous Vector Fields in Sequence Spaces

2022/04/23 by Oleg Zubelevich, Zubelevich, Oleg
Engineering · Mathematics · #34G20 #46A04 #46A45 #47H07 #47J35 #58D25 #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Thin Films #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2204.11037

openalex publication_date 2022/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Degree theory for discontinuous operators
• Beyond Peano's theorem: a variational look at discontinuous ODE systems
• Evolution Differential Equations in Fréchet Space with Schauder Basis
• New fixed point theorem and its application to ODE
• Note on the existence theory for evolution equations with pseudo-monotone operators