Cauchy problem for the nonlocal Schrödinger equation. I

The Cauchy problem for the nonlocal nonlinear Schrödinger equation is studied. The case of smooth initial data is considered. The existence of classical solutions in the large is proved for the case of the bounded operator. The conditions are studied which provide the existence of classical solutions in the case of unbounded conservative or dissipative operators. The existence of generalized solutions is proved for conservative operators.