Correction: Ricceri, B. A Class of Equations with Three Solutions. Mathematics 2020, 8, 478

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Correction: Ricceri, B. A Class of Equations with Three Solutions. Mathematics 2020, 8, 478
by Biagio Ricceri
Department of Mathematics and Informatics, University of Catania, Viale A. Doria 6, 95125 Catania, Italy
Mathematics 2021, 9(1), 101; https://doi.org/10.3390/math9010101
Received: 15 October 2020 / Accepted: 22 December 2020 / Published: 5 January 2021
(This article belongs to the Special Issue Nonlinear Functional Analysis and Its Applications)
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The author wishes to make the following correction to this paper [1]:
Everywhere it occurs, the phrase “for every convex set S⊆H10(Ω) dense in H10(Ω)” should be replaced with “for every convex set S⊆L∞(Ω) dense in L2(Ω)”.
Actually, thanks to (b) of Theorem 2, condition (1) can be weakened to
lim∥x∥X→+∞⟨φ(x),y⟩YI(x)=0
(1)for all y in a convex and dense set V⊆Y. Then, in the conclusion of Theorem 1, we can replace “S⊆Y” with “S⊆V”. Finally, in the proof of Theorem 3, we take V=L∞(Ω), so that condition (a) is actually enough to prove equality (1).
The author would like to apologize for any inconvenience caused to the readers by these changes. The changes do not affect the scientific results. The original article has been updated.