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In this contribution we consider sequences of monic polynomials orthogonalwith respect to the standard Freud-like inner product involving a quarticpotential  $\left\langlep,q\right\rangle_{M}=\int_{\mathbb{R}}p(x)q(x)e^{-x^{4}+2tx^{2}}dx+Mp(0)q(0).$  We analyze some properties of these polynomials, such as the ladder operatorsand the holonomic equation that they satisfy and, as an application, we give anelectrostatic interpretation of their zero distribution in terms of alogarithmic potential interaction under the action of an external field. It isalso shown that the coefficients of their three term recurrence relationsatisfy a nonlinear difference string equation. Finally, an equation of motionfor their zeros in terms of their dependence on $t$ is given.

On polynomials associated with an Uvarov modification of a quartic potential Freud-like weight