One method to show the existence of ω-periodic system is given. This method is based on the ultimately boundedness of the solution of the systems. By using comparing theorem and discussing some one dimensional equati...One method to show the existence of ω-periodic system is given. This method is based on the ultimately boundedness of the solution of the systems. By using comparing theorem and discussing some one dimensional equations the main results are obtained.展开更多
The present article considers the existence of T-periodic solutions for the following Lienard equation with delay.where h≥0 is a constant, (Rn, R), (Rn, R), (R, Rn), p(t+T)=p(t) for a constant T>0 and . By use of ...The present article considers the existence of T-periodic solutions for the following Lienard equation with delay.where h≥0 is a constant, (Rn, R), (Rn, R), (R, Rn), p(t+T)=p(t) for a constant T>0 and . By use of V-function and coincidence degree. The result proposed by Ge Weigao is extended to the case of delay-differential system in the papee. One feature of our result is that the delay has a notable impact on the existence of periodic soultion.展开更多
In this paper, it is discussed the model of a kind of nonlinear differential, equation d s d t=1-s-x 1s 0δQ 2(m 1s 0sk 1+s 0s-k) d x 1 d t=x 1Q(m 1s 0sk 1+s 0s-k)-x 1-x 2m 2x 1/Qk 2+x 1/Q...In this paper, it is discussed the model of a kind of nonlinear differential, equation d s d t=1-s-x 1s 0δQ 2(m 1s 0sk 1+s 0s-k) d x 1 d t=x 1Q(m 1s 0sk 1+s 0s-k)-x 1-x 2m 2x 1/Qk 2+x 1/Q d x 2 d t=x 2Q m 2x 1/Qk 2+x 1/Q-x 2.It is proved that the system is exist at least one stable periodic solution on under the following condition:m 2x * 2(k 1δ+s 0δ-Qλ 2-x * 2) 2】m 1δk 1(k 2+Q 2λ 2) 2.Furthermore, ifm 2x * 2(k 1δ+s 0δ-Qλ 2-x * 2) 2【m 1δk 1(k 2-Q 2λ 2) 2mold true them equilibrium point (s *,x * 1,x * 2)∈ set Ω is global asymptotic stable.展开更多
The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are ...The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are established for the existence of periodic solutions and some previous results are extended.展开更多
J.Kaplan and J.Yorke's method is extended to establish the exis- tence of many and infinitely many periodic solutions for the DDEs (t) =±f(x(t-1))±f(x(t-2))and (t)=±f(x(t-1).
Existence criteria is established for the periodic solution of the nonlinear neutral delay differential equation x′(t)=f(t,x(t),x(t-τ 1(t)),x′(t-τ 2(t)))+p(t) by means of an abstract continuous theorem of k-set ...Existence criteria is established for the periodic solution of the nonlinear neutral delay differential equation x′(t)=f(t,x(t),x(t-τ 1(t)),x′(t-τ 2(t)))+p(t) by means of an abstract continuous theorem of k-set contractive operator and some analysis technique.展开更多
文摘One method to show the existence of ω-periodic system is given. This method is based on the ultimately boundedness of the solution of the systems. By using comparing theorem and discussing some one dimensional equations the main results are obtained.
文摘The present article considers the existence of T-periodic solutions for the following Lienard equation with delay.where h≥0 is a constant, (Rn, R), (Rn, R), (R, Rn), p(t+T)=p(t) for a constant T>0 and . By use of V-function and coincidence degree. The result proposed by Ge Weigao is extended to the case of delay-differential system in the papee. One feature of our result is that the delay has a notable impact on the existence of periodic soultion.
文摘In this paper, it is discussed the model of a kind of nonlinear differential, equation d s d t=1-s-x 1s 0δQ 2(m 1s 0sk 1+s 0s-k) d x 1 d t=x 1Q(m 1s 0sk 1+s 0s-k)-x 1-x 2m 2x 1/Qk 2+x 1/Q d x 2 d t=x 2Q m 2x 1/Qk 2+x 1/Q-x 2.It is proved that the system is exist at least one stable periodic solution on under the following condition:m 2x * 2(k 1δ+s 0δ-Qλ 2-x * 2) 2】m 1δk 1(k 2+Q 2λ 2) 2.Furthermore, ifm 2x * 2(k 1δ+s 0δ-Qλ 2-x * 2) 2【m 1δk 1(k 2-Q 2λ 2) 2mold true them equilibrium point (s *,x * 1,x * 2)∈ set Ω is global asymptotic stable.
文摘The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are established for the existence of periodic solutions and some previous results are extended.
文摘J.Kaplan and J.Yorke's method is extended to establish the exis- tence of many and infinitely many periodic solutions for the DDEs (t) =±f(x(t-1))±f(x(t-2))and (t)=±f(x(t-1).
文摘Existence criteria is established for the periodic solution of the nonlinear neutral delay differential equation x′(t)=f(t,x(t),x(t-τ 1(t)),x′(t-τ 2(t)))+p(t) by means of an abstract continuous theorem of k-set contractive operator and some analysis technique.
