  In this article a technique for constructing $p$-ary bent functions from
near-bent functions is presented. Two classes of quadratic $p$-ary functions
are shown to be near-bent. Applying the construction of bent functions to these
classes of near-bent functions yields classes of non-quadratic bent functions.
We show that one construction in even dimension yields weakly regular bent
functions. For other constructions, we obtain both weakly regular and
non-weakly regular bent functions. In particular we present the first known
infinite class of non-weakly regular bent functions.
