Directions of Mathematical Research in Nonlinear Circuit Theory

In this paper we wish to present a potpourri of problems of some interest and difficulty arising in the field of nonlinear circuit theory. Perhaps the only sensible way to catalogue scientific problems is in terms of "solved or unsolved." Yet this classification is itself a very subjective one, dependent upon the times and the fashions. Recall the dictum of Poincaré that the solutions of one generation are the problems of the next. In this paper, we have attempted, for the sake of convenience, to group categories of problems under the headings of "descriptive," "control," "stochastic," and so forth. Convenient as some of this nomenclature is, it should be regarded with a certain amount of suspicion. Most significant problems blithely cut across these artificial boundaries within fields of specialization, and within science itself. In these days of rapidly and dramatically changing technology it would be rather brash to attempt to predict the type of mathematics that will be most urgently required even ten years from now. It is, however, fairly safe to look about and note the requirements of the present and of five years back. The difficulties that abound render a certain time lag inevitable, and it may well be that new scientific developments may render fields obsolete and mathematical solutions for problems within those fields unnecessary before they are even obtained.