Schneider (Math. Nachr. 60 (1974), 167–180) has established the following result. Consider the mixed type equation
in G ⊂ R2 which is a simply connected region, bounded for y > 0 by a piece-wise smooth curve Γ0 connecting the points A(0, 0) and B(1, 0), and for y < 0 by the solutions of k(y).(dy)2 + (dx)2 = 0 which meet at the point G(½, yc), such that for ,
S(x, y) = F(yy) + 8λ·(k/k′)2 > 0 in Ḡ ∩ {y < 0}, “Schneider's Condition”, where F(y) = 1 + 2(k/k′)′, and such that S = S(x, y) is integrable in G2, “Frankl's Condition”. Then the Tricomi Problem (T): L[u] = f with has a weak solution u ∈ L2(Ḡ) and the Adjoint Tricomi Problem (T+): L+[w] = f with has at most one semistrong solution.
In this present paper we get the above result of Schneider in a much more generalized way, so that here our uniqueness theorem and existence results include cases where S(x, y) may be negative in G2.