Correct problems in a layer with differential operators under the boundary condition - Fardigola , L. V. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
We obtain a criterion for the well-posedness of a boundary-value problem in the layer ℝn × [0, T] for a linear differential evolution equation with constant complex coefficients in the class of functions of power growth under a two-point condition that contains two arbitrary differential operators with respect to space variables (one of the operators can be zero). Examples of well-posed and ill-posed problems of this form are given.