Relations between solutions of Einstein 5-dim gravity coupled to a dilaton field with a potential with holographic renormalization group flow equations are discussed. Applications of these holographic renormalization group flow equations to a hot and dense quark-gluon plasma (QGP) are considered. We especially focus on presenting a few examples typically used in the holographic description of the QGP. We study the influence of the chemical potential and anizotropy on the holographic $\beta$-function in these examples.