On nonuniqueness of solutions of the von Kármán equations

Abstract : A constructive method is used to study the nonuniqueness of solutions of a pair of non-linear partial differential equations (the von Karman equations) governing the deflections of a thin, flat, elastic plate that is clamped at the edges and subjected to combined normal and edge loading. In addition, although in general the solutions of the above problem are not unique, it is shown that, for sufficiently small normal and edge loading, uniqueness does prevail. (Author)