ON VARIATIONAL-PRINCIPLES FOR NONLINEAR PARTIAL-DIFFERENTIAL EQUATIONS IN COMPLEX-SPACES

The necessary and sufficient conditions for an abstract equation in a complex Banach space to admit a variational principle, which one of us described in a previous paper, are here applied to a system of nonlinear partial differential equations of arbitrary order in a complex L2 space. More specific and helpful conditions are thus obtained. General consequences and special implications for some classes of nonlinear Schrodinger equations are also discussed and differences from an analogous result valid only in real spaces are put in evidence.