Showing papers in "Czechoslovak Mathematical Journal in 1975"

Linear boundary value type problems for functional-differential equations and their adjoints

Abstract: where — o o < a < b < o o and the functions P(f, ,9), G{t, s), A{t), B{t) and f(t) fulfil some natural assumptions. In particular, we derive their adjoints and in some special cases prove the Fredholm alternative. (The results of A. HALANAY [5] or E. A. LiFSic [9] on the existence of periodic solutions to the equation (0,1) and the results of [12] on integral boundary value problems for ordinary integro-differential equations are included.) Our approach is based on the ideas of D. WEXLER [14] and ST. SCHWABIK [ U ] and differs from that of A. Halanay [6] or D. HENRY [8] (cf. also J. K. HALE [7]). The adjoint problems obtained seem to be more natural than those of D. Henry [8] and follow directly from the principles of functional analysis. (It is shown that after some artificial steps our adjoint reduces to that of D. Henry.) Initial functions are continuous on [a — r, a] or of bounded variation on [a — r, a\. In § 4 boundary value type problems for hereditary differential equations considered in the sense of M. C. DELFOUR, S. K. MITTER [3] (with square integrable initial functions) are treated.