Oscillation and nonoscillation in a nonautonomous delay-logistic equation

Quarterly of Applied Mathematics - Tập 46 Số 2 - Trang 267-273
B. G. Zhang1, K. Gopalsamy2
1Shandong College of Oceanography, People's Republic of China) AND
2The Flinders University of south Australia

Tóm tắt

Sufficient conditions are obtained for the delay-logistic equation x ˙ ( t ) = r ( t ) x ( t ) [ 1 x ( t τ ( t ) ) / K ] \dot x\left ( t \right ) = \\ r\left ( t \right )x\left ( t \right )\left [ {1 - x\left ( {t - \tau \left ( t \right )} \right )/K} \right ] to be respectively oscillatory and nonoscillatory.

Từ khóa


Tài liệu tham khảo

Èl′sgol′ts, L. E., 1973, Introduction to the theory and application of differential equations with deviating arguments

Gopalsamy, K., 1986, Oscillations in a delay-logistic equation, Quart. Appl. Math., 44, 447, 10.1090/qam/860898

Jones, G. Stephen, 1962, The existence of periodic solutions of 𝑓′(𝑥)=-𝛼𝑓(𝑥-1){1+𝑓(𝑥)}, J. Math. Anal. Appl., 5, 435, 10.1016/0022-247X(62)90017-3

Kakutani, S., 1958, On the non-linear difference-differential equation 𝑦′(𝑡)=[𝐴-𝐵𝑦(𝑡-𝜏)]𝑦(𝑡), 1

Koplatadze, R. G., 1982, Oscillating and monotone solutions of first-order differential equations with deviating argument, Differentsial\cprime nye Uravneniya, 18, 1463

Kulenović, M. R. S., 1987, On oscillation of nonlinear delay differential equations, Quart. Appl. Math., 45, 155, 10.1090/qam/885177

Ladde, G. S., 1987, Oscillation theory of differential equations with deviating arguments, 110

Shevelo, V. N., 1978, {\cyr Ostsillyatsiya resheni\u{i}} {\cyr differentsial\cprime nykh uravneni\u{i}} {\cyr s otklonyayushchimsya argumentom}

Wright, E. M., 1955, A non-linear difference-differential equation, J. Reine Angew. Math., 194, 66, 10.1515/crll.1955.194.66