## The functional-differential equation $$y'(x)=ay(\lambda x)+by(x)$$.(English)Zbl 0236.34064

### MSC:

 34K10 Boundary value problems for functional-differential equations 34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
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### References:

 [1] L. Fox, D. F. Mayers, J. R. Ockendon and A. B. Tayler, On a functional differential equation, J. Inst. Math. Appl. (to appear). · Zbl 0251.34045 [2] Kurt Mahler, On a special functional equation, J. London Math. Soc. 15 (1940), 115 – 123. · Zbl 0027.15704 [3] Proceedings United States-Japan Seminar on Differential and Functional Equations, Held at the University of Minnesota, Minneapolis, Minn., June 26-30, 1967. Edited by William A. Harris, Jr. and Yasutaka Sibuya, W. A. Benjamin, Inc., New York-Amsterdam, 1967. [4] N. G. de Bruijn, The asymptotically periodic behavior of the solutions of some linear functional equations, Amer. J. Math. 71 (1949), 313 – 330. · Zbl 0033.27002 [5] N. G. de Bruijn, On some linear functional equations, Publ. Math. Debrecen 1 (1950), 129 – 134. · Zbl 0036.19501 [6] N. G. de Bruijn, The difference-differential equation F’(x) = e. I, II, Nederl. Akad. Wetensch. Proc. Ser. A 56 = Indag. Math. I5 (1953), 449-464. MR 15, 629. · Zbl 0053.38703 [7] E. W. Bowen and G. R. Morris, private communication. [8] Paul O. Frederickson, Global solutions to certain nonlinear functional differential equations, J. Math. Anal. Appl. 33 (1971), 355 – 358. · Zbl 0191.15302 [9] P. O. Frederickson, Analytic solutions for certain functional-differential equations of advanced type (to appear). · Zbl 0191.15302 [10] Richard Bellman and Kenneth L. Cooke, Differential-difference equations, Academic Press, New York-London, 1963. · Zbl 0105.06402 [11] Laurent Schwartz, Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, No. IX-X. Nouvelle édition, entiérement corrigée, refondue et augmentée, Hermann, Paris, 1966 (French). · Zbl 0962.46025
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