A sufficient condition for the local solvability of a linear partial differential operator with double characteristics

AbstractIt is shown that a sufficient condition for the local solvability of an operator P(x, Dx) = Pm2 + P2m − 1, where P is an mth-order homogeneous operator of principal type with real coefficients, is that the imaginary part of the subprincipal symbol of P has constant sign near any null-bicharacteristic curve of Pm, and that the real part of the subprincipal symbol is not equal to zero when the imaginary part is