This paper concerns, under consideration of some well-known results, existence and uniqueness of single-wave-form solutions for series arrays of \(N\) Josephson junctions coupled through general RLC loads. The proof is based on the reduction of the problem to a fixed-point equation on an appropriately chosen Hilbert space and uses an extension of Brouwer’s fixed point theorem.
The authors apply this technique to prove that single-wave-form solutions exist when the bias current \(I\) is greater than \(1\) and are essentially unique when either \(N\) or \(I\) is large.
They continue their presentation of results to give explicit examples of series arrays which possess several distinct single-wave-form solution. Finally with an application of Newton’s method, a numerical construction of multiple signal-wave-form solution is given. In the concluding section some open questions are presented.