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

The author wishes to make the following correction to this paper [1]:

Everywhere it occurs, the phrase “for every convex set $S\subseteq H_0^1(\Omega )$ dense in $H_0^1(\Omega )$” should be replaced with “for every convex set $S\subseteq L^{\infty }(\Omega )$ dense in $L^2(\Omega )$”.

Actually, thanks to $\left(b\right)$ of Theorem 2, condition $\left(1\right)$ can be weakened to

$$\underset{{\parallel x\parallel }_X\to +\infty }{lim}\frac{{\langle \phi \left(x\right),y\rangle }_Y}{I\left(x\right)}=0$$

(1)

for all y in a convex and dense set $V\subseteq Y$. Then, in the conclusion of Theorem 1, we can replace “$S\subseteq Y$” with “$S\subseteq V$”. Finally, in the proof of Theorem 3, we take $V=L^{\infty }(\Omega )$, so that condition $\left(a\right)$ 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.