Corrigendum to "The splitting lemmas for nonsmooth functionals on Hilbert spaces II. The case at infinity" (Topol. Methods Nonlinear Anal. 44 (2014), 277-335)

Abstract

We show how to correct errors in [1, § 4] caused by the incorrect inequality [1, (4.2)].Here we only point out main corrected points and refer readers to [2, § 4] for a completely rewritten version of [1, § 4]. After removing the incorrect inequality [1, (4.2)] some corrections to the arguments in [1, § 4] should be made.• The original (q * 1 ) and (q * 3 ) should be replaced by the following slightly stronger ones:(q * 1 ) There exist constants c 1 > 0, r ∈ (0, 1) and a function E ∈ L 2 (Ω) such that |q(x, t)| ≤ E(x) + c 1 |t| r for almost x ∈ Ω and for all t ∈ R. (q * 3 ) For almost every x ∈ Ω the function R t → q(x, t) is differentiable and Ω × R (x, t) → q t (x, t) := ∂q ∂t (x, t) is a Carthéodory function. There exist s ∈ (n/2, ∞), ∈ L s (Ω), and a bounded measurable h : R → R such that h(t) → ∈ R as |t| → ∞ and |q t (x, t)| ≤ (x)h(t) for almost every x ∈ Ω and for all t ∈ R.