Abstract：First， by solving the problem of so called generalized second order singular distributed parameter system， the defifinition of generalized cosine operator function was introduced， and some basic properties of the generalized cosine operator function were characterized. Then the generation theory， approximation and perturbation theory and ergodic theory were also studied. Lastly， the well-posedness problem of generalized second order Cauchy problem was investigated.
2020, Vol. 54 
