## On the nonlinear differential-difference equation $$f'(x)=-\alpha f(x- 1)(1+f(x))$$.(English)Zbl 0106.29503

### Keywords:

ordinary differential equations
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### References:

 [1] Bellman, R.E, A survey of the mathematical theory of time-lag retarded control, and hereditary processes, (1954), The RAND Corp Santa Monica, Calif · Zbl 0056.36501 [2] Lord, Cherwell; Lord, Cherwell, Number of primes and probability considerations, Nature (London), Nature (London), 150, 121, (1942) · Zbl 0063.00838 [3] Cunningham, W.J, A non-linear differential-difference equation of growth, (), 709-713 · Zbl 0055.31601 [4] {\scJones, G. S.} The existence of periodic solutions of f′(x) = −αf(x − 1) {1 + 1f(x)}. J. Math. Anal. and Appl. in press. [5] Jones, G.S, Asymptotic behavior and periodic solutions of a nonlinear differential-difference equation, () · Zbl 0132.32403 [6] Kakutani, S; Markus, L, On the non-linear difference-differential equation y′(t) = {A − by(t − τ)} y(t), (), 1-18 · Zbl 0082.30301 [7] Wright, E.M, A non-linear difference-differential equation, J. reine angew. math., 194, 66-87, (1955) · Zbl 0064.34203 [8] Wright, E.M, A functional equation in the heuristic theory of primes, Math. gaz. (London), 45, No. 351, 15-16, (1961) · Zbl 0125.02602
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