ABSTRACT
Similarly, the boundary conditions (9.2) may then be written in the form
(9.5) where P+ (respectively P_) denotes the restriction operator from X = X([ -1,1]) onto X+ = X([O, 1]) (respectively onto X_ = X([ -1,0]).
As pointed out in Subsection 1.1, a crucial point when passing from the problem (9.1)/(9.2) to the problem (9.3)/(9.5) is the appropriate choice of the function space X. It is clear that taking the space X = C([-l,l]) of continuous functions is too restrictive. In fact, even if all functions c, k, and / in (9.1) are zero, and the boundary functions q, and 1/J in (9.2) are continuous, there is certainly no solution of (9.1)/(9.2) if the "glueing condition"
