Displaying similar documents to “On the decay rate of solutions of non-autonomous differential systems.”

Nonlinear exponential twists of the Liouville function

Qingfeng Sun (2011)

Open Mathematics

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Let λ(n) be the Liouville function. We find a nontrivial upper bound for the sum ∑ X ⩽ n ⩽ 2 X λ ( n ) e 2 π i α n , 0 ≠ α ∈ ℝ The main tool we use is Vaughan’s identity for λ(n).

Decay rates of Volterra equations on ℝN

Monica Conti, Stefania Gatti, Vittorino Pata (2007)

Open Mathematics

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This note is concerned with the linear Volterra equation of hyperbolic type ∂ t t u ( t ) - α Δ u ( t ) + ∫ 0 t μ ( s ) Δ u ( t - s ) d s = 0 on the whole space ℝN. New results concerning the decay of the associated energy as time goes to infinity were established.