We discuss the Volterra integral equation x'(t) + λ ∫₀ᵗ a(t - τ )x(τ )dτ = k,λ ≥ λ ₀ > 0. We find conditions under which solutions are bounded on \ 0 ≤ t < ∞ \, uniformly in λ. We deduce results on the asymptotic behavior of certain Volterra equations in Hilbert space arising, for example, in viscoelasticity.
No takes yet. Share an insight, caveat, or question.
Kenneth B. Hannsgen (1973) studied this question.
Synapse has enriched 5 related papers. Consider them for comparative context: