Dear All,
I have a question regarding the the existence and uniqueness of a system of linear Volterra integral equations.
Does the solution exist? Is it unique?
What are the conditions on the kernels for the existence and uniqueness of this system of equations?
The equation is written in the attached file.
I would appreciate your help greatly. Thank you.
Sarah
I am not an expert in integral equations, but it seems that, more or less, the same argument of the proof of local existence and uniqueness for Cauchy problems can be applied, i.e., that the right-hand side is a contraction (for example, in (L^\infty)^n) for x small enough.
From practical perspective I feel that the uniqueness of the solution would depend on how many parameters you have in the set of equations. In one case, I had 5 parameters. It is like trying to fit in a 5 dimensional space. Such solutions cannot be unique. However, they do shed light on various other aspects and that itself is valuable.
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