We employ an analytical approach introduced by López to determine the anomalous scaling exponent of the growth equation with a generalized conservation law in both the weak-and strong-coupling regimes,which included the Kardar-Parisi-Zhang(KPZ),Sun-Guo-Grant(SGG),and molecular beam epitaxy(MBE)equations as special cases and allows for a unified treatment of growth equations.

The results of the anomalous exponents are employed in several typical local growth equations,which include the Kardar-Parisi-Zhang(KPZ)equation,linear equation and Lai-Das Sarma-Villain(LDV) equation, to judge the condition of anomalous scaling behaviors.

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