On subharmonic synchronization of nearly-linear systems
Hirsh Cohen · Quarterly of Applied Mathematics · 1955
function of the limit stresses and a solution of problem (P).Because of the uniqueness $ is given by (2.4).This verification as well as the uniqueness proof are by no means superfluous.In fact, the solution ceases to be unique if the condition of boundedness is dropped.Consider for example the function **(z, r) = r4(l -*2 -r2)[{z -l)2 + r2]"7'2, (5.1) which satisfies (2.1) in H and assumes the boundary value 0 everywhere, except at B, where 3>* = 0(b~2).This stress function corresponds to a singular self-equilibrated system of forces at B. Superposing (2.4) and (4.2) we obtain a function which fulfills all conditions of problem (P) except boundedness.In the terminology of E. Sternberg and F. Rosenthal [5], who treated the case of concentrated loads, it is a "pseudosolution"of the physical problem.