On the solvability of some systems of integro-differential equations with and without a drift

Abstract

We prove the existence of solutions for some integro-differential systems containing equations with and without drift terms in the $H^2$ spaces by virtue of the fixed point technique when the elliptic equations contain second order differential operators with and without Fredholm property, on the whole real line or on a finite interval with periodic boundary conditions. Let us emphasise that the study of the system case is more complicated than of the scalar situation and requires to overcome more cumbersome technicalities.

Keywords:

• Solvability conditions
• non-Fredholm operators
• integro-differential systems
• drift terms

2020 Mathematics Subject Classification:

• 35J61
• 35R09
• 35K57

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

All data generated or analysed during this study are included in this published article.

Additional information

Funding

V. V. is grateful to Israel Michael Sigal for the partial support by the NSERC grant NA 7901.