@MIchael Renardy To clarify, normally I would brouse books in the library to try and find somthing, but due to covid I have to request textbooks, and wait a week before I get access to them. This prevents me from flicking through promising textbooks, and finding ones with a promising contents/index item. It would be very helpful if I could know, a week in advance of getting a book, whether it has the information I need.

@Michael Renardy I've looked in Evans, Friedman and Garabedian, none of them discuss the type of system specified above. Looking through papers published in the last 10 years or so they all concern themselves with more sofisticated systems, so I assume this system has been delt with. If you know many textbooks that give existance and uniquness of the equations given, or reference where this was prooved, then perhaps you could list a few? Even one?