LAUSR

In the article titled “Noncoercive Perturbed Densely De ned Operators and Application to Parabolic Problems” [1], there was an error in eorem 8. e operator L : X ⊇ D(L) → X is assumed to be linear, closed, densely de ned, and monotone. However, it is required to replace this assumption on L by the condition that L : X ⊇ D(L) → X is linear maximal monotone. It is known due to Brèzis (cf. Zeidler [2, eorem 32. L, p.897]) that every linear maximal monotone operator is densely de ned and closed. However, the converse is not generally true unless L is monotone. In addition to conditions on S in eorem 8 in [1], monotonicity assumption on S (with S(0) = 0) is required. e condition ⟨Lx + Sx, x⟩ ≥ −d‖x‖ for all x ∈ D(L) is not required as it is automatically satis ed with d = 0 because of monotonicity of L and S with (L + S)(0) = 0. As a result, eorem 8 in [1] is restated and replaced by eorem 1 as follows.