On abstract Volterra equations with kernels having a positive resolvent

We consider the nonlinear abstract Volterra equation of convolution type: V $$u(t) + b * Au(t) = u_0 + b * g(t), t \geqq 0,$$ whereA ism-accretive in Banach spaceX, b is a given real kernel,u ₀ andg are given. Boundedness and asymptotic properties of the solutions are established under the assumption that the kernel satisfies certain natural positivity conditions.