Semilinear evolution equations of second order via maximal regularity.

Cuevas, Claudio; Lizama, Carlos

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In this paper we consider several conditions for sequences of points in M(H ∞) and establish relations between them. We show that every interpolating sequence for QA of nontrivial points in the corona $M (H^{\infty}) ∖ 𝔻$ of H ∞ is a thin sequence for H ∞, which satisfies an additional topological condition. The discrete sequences in the Shilov boundary of H ∞ necessarily satisfy the same condition.

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Asymptotic properties of the half-linear difference equation $Δ (a_{n} | Δ x_{n} |^{α} s g n Δ x_{n}) = b_{n} {| x_{n + 1} |}^{α} s g n x_{n + 1} (*)$ are investigated by means of some summation criteria. Recessive solutions and the Riccati difference equation associated to $(*)$ are considered too. Our approach is based on a classification of solutions of $(*)$ and on some summation inequalities for double series, which can be used also in other different contexts.

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