Periodic solutions of some linear evolution svstems of natural differential equations on 2-dime

Abstract

In this paper we study periodic solutions of the equation7/A \; (; + aa )u@,t) : uG(u - f), (1)with conditionsut-o:'tlt-bt [ @@),r) d,n:o (2)Jx over a Riemannian manifold X. where Gu(r,t) :, I s@,y)u(y)dyJx__q is an integral operator, u(n , t) is a differential form on X , A : i(d+ 5) is a natural differential operator in X. We consider the case when X is a tore fI2. It is shown that the set of parameters (u,b) for which the above problem admits a unique solution is a measurable set of complete measureinCx]R+