On the First Mixed Boundary Value Problems for Linear Equations with Generalized Right Invertible Operators

Pham Thi Bach Ngoc

In this paper we consider a first mixed boundary value problem (FMBVP) (cf. [3])  with generalized right invertible operator V for the operator Q[V]as follows. 

Find all solutions of the problem

Q[V]x  :=VmAmnVnx = y,    y X
FjVjx  = yj,   yjker V  are given,   j = 0, ..., M+N-1,

where M, N , Am  L0(X),  AMN = I , AmnXM+N-n Xm , Xj: = dom Vj.