The Solvability of the Boundary Value Problem of the Four Elements with the Carleman Shift and Complex-conjugate Values

Abstract

To following boundary value problem a(t)\overline{Φ^+(t)} + b(t)Φ^+[α(t)] + c(t)\overline{Φ^-(t)} + d(t)Φ^-[a(t)] = f(t) this paper has given out the number of linearly independent solutions and the conditions of solvability, so as to deepen the study of the problem to the same level as that of following problem a(t)\overline{Φ^+(t)} + b(t)Φ^+(t) + c(t)\overline{Φ^-(t)} + d(t)Φ^-(t) = f(t)