I have a function $f:{\mathbb R}\rightarrow {\mathbb R}_+$ which has a unique maximum at $x=0$. $f$ can be symmetric or asymmetric. I am interested on the mollified-f function

$$\tilde{f}(x)=\int_{-\epsilon}^{\epsilon}\varphi(y)f(x-y)dy,\,\,\, \epsilon>0$$

I wonder if there are general results on the Mollifier $\varphi$, such that $\tilde{f}$ also has a unique maximum (not necessarily at $0$).