Cauchy problem for complete second-order hyperbolic differential equations with variable domains of operator coefficients

Abstract

Complete second-order hyperbolic differential equations with constant domains of operator co- efficients were investigated in [1, 2]. In the case of variable domains of operator coefficients, second-order hyperbolic differential equations with a two-term leading part were analyzed in [3-5]. In the present paper, we investigate second-order hyperbolic differential equations with a three-term leading part in the case of variable domains of operator coefficients.