Sufficient conditions are given
to ensure the existence of solutions for the boundary value problem
![∫
t
y(t) = T(t)ϕ (0)+ 0 T(t− s)F(ys)ds 0 ≦ t ≦ b](a160x.png) | (1) |
It is assumed that T(t), t ≧ 0, is a strongly continuous semigroup of bounded linear
operators on the Banach space B and T(t), t ≧ 0, has infinitesimal generator A. The
function F is continuous from C to B and M and N are bounded linear operators
defined on C.
|