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I study an Extended Periodic Anderson Model (EPAM) with non-localhybridisation, $V_{fc}$, and a coulomb interaction, $U_{fc}$, between localised$f$ electrons and wide band conduction ($c$) electrons. Within DMFT, a quantumphase transition (QPT) driven by soft $f$-valence fluctuations, accompanied bya discontinuous jump in the Fermi volume, is found as $V_{fc}$ is tuned acrossa critical value. Near the associated QCP, an unconventional superconductiveinstability, driven by these extended, singular valence fluctuations, naturallyemerges. {\it All} these phenomena are representative of observations inpressurised $CeCu_{2}Si_{2}$.

Valence Fluctuation Driven Non-Fermi LIquid Behavior and Unconventional Superconductivity in Pressurized CeCu_{2}Si_{2}