Time-varying cosmological term

We present the case of time-varying cosmological term using the Lagrangian formalism characterized by a scalar field 0 with standard kinetic energy and arbitrary potential V(phi). This model is applied to Friedmann-Robertson-Walker (FRW)cosmology. Exact solutions of the field equations are obtained by a special ansats to solve the Einstein-Klein-Gordon equation and a particular potential for the scalar field and barotropic perfect fluid. We present the evolution on this cosmological term with different scenarios.