ERGODIC THEOREMS FOR MIXIMAL MONOTONE OPERATORS OF NON-LINEAR VOLTERRA INTEGRAL EQUATIONS IN HILBERT SPACES = 힐버트 공간에서 볼테라 적분방정식의 최대 작용소에 대한 에르고딕 정리

다국어 초록 (Multilingual Abstract)

We consider the non-linear Volterra integral equation:
(V) u(t)+ ?? b(t-s)Au(s)ds∋F(t), t>0,
where b, A and F are given and u is the known taking values in a real Hilbert space H. The kernel b is real-valued function and F takes [0.∞) into H. The mapping A is a non-linear monotone operator in H.
We study that the Cesaro mean of the solution for (V) converges weakly and almost strongly in H. In order to prove these results, we shall make the equivalent form:
??+Au(t)∋αf(t)+k*f(t)+u0k(t)-k(0)u(t)-u*k`(t), u(0)=u0,
where F`(t)=f(t), k*f(t) is the convolution of k and f and α, k defined by αb(t)+αk*b(t)=1. α>0, which is the generalization of results by M.G.Crandall and J.A.Nohel.