caa a22 4500 386382646 CHVBK 20180307112048.0 cr unu---uuuuu 161130s1989 xx s 000 0 eng 10.1017/S0308210500024148 doi S0308210500024148 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500024148 Nussbaum Roger D. Mathematics Department, Rutgers University, New Brunswick, New Jersey, U.S.A Wright's equation has no solutions of period four [Elektronische Daten] [Roger D. Nussbaum] Let N:ℝ→ℝ be a locally Lipschitzian map such that (y + l)N(y)>0 for all y ≠ -1 and such that N(y)=1 + y for - 1 ≦ y ≦ 3. For any positive number α the equation y'(t) αy(t-1)N(y(t)) has, aside from the constantsolutions y(t) ≡ -1, and y(t) ≡-1 solution y(t) such that y(t + 4) = y(t) for all real t If N(y) = 1 + y for all y, one obtains Wright's equation, which isknown to have periodic solutions of minimal period p (depending on α) arbitrarily close to 4. Some results concerning nonexistence of periodic solutions of period 4 of other differential-delay equations are also proved. In all cases the method of proof consists in analysing an associated fourth-order system of ordinary differential equationsand showing that this system has no nonconstant periodic solutions. Copyright © Royal Society of Edinburgh 1989 Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 113/3-4(1989), 281-288 0308-2105 113:3-4<281 1989 113 PRM https://doi.org/10.1017/S0308210500024148 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500024148 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Nussbaum Roger D. Mathematics Department, Rutgers University, New Brunswick, New Jersey, U.S.A NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 113/3-4(1989), 281-288 0308-2105 113:3-4<281 1989 113 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge