We consider the initial value problem for a possibly degenerate in-tegrodifferential equation in L2(Ω) (eqution found) where M(t) = M0M1(t) is the multiplication operator by the function m(x, t) = m0(x)m1(x, t), m0(x) ≥ 0, m1(x, t) ≥ c > 0, L(t) is the realization in L2(Ω) of a second-order strongly elliptic operator in divergence form with Dirichlet or Neumann boundary conditions for all t, and B(t, s) is a linear differential operator of order ≤ 2 for each (t, s), 0 ≤ s ≤ t ≤ T, Ω being a bounded open set in Rn with a smooth boundary. We also establish a corresponding result in Lp(Ω), 1 < p < 3/2, related to Dirichlet boundary condition, only.

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