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    {\bf A One Perturbation Variational Principle and Applications}
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    {\bf Abstract}
   
    We study a variational principle with a \emph{common} perturbation
    function $\varphi$  for \emph{all} proper lower semicontinuous
    extended real-valued functions $f$  on a metric space $X$.
   
    \begin{itemize}
    \item Necessary and  sufficient conditions are given  for the
    perturbed  $f+\varphi$ to attain its minimum.
   
     \item For separable Banach space we may use  a  perturbation function
     that is also convex and \emph{Hadamard-like} differentiable.
   
     \item We give three applications  to differentiability of convex
     functions on separable and more general Banach spaces.

    \item We pose various open questions.  \end{itemize}
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