Partial cooperation formulation is a more viable option than optimistic＇s and pessimistic＇s to solve an ill-posed bilevel programming problem.Aboussoror＇s partial cooperation model uses a constant as a cooperation ...Partial cooperation formulation is a more viable option than optimistic＇s and pessimistic＇s to solve an ill-posed bilevel programming problem.Aboussoror＇s partial cooperation model uses a constant as a cooperation index to describe the degree of follower＇s cooperation.The constant only indicates the leader＇s expectation coefficient for the follower＇s action,not the follower＇s own willingness.To solve this situation,a new model is proposed by using the follower＇s satisfactory degree as the cooperation degree.Then,because this new cooperation degree is a function which is dependent on the leader＇s choice and decided by the follower＇s satisfactory degree,this paper proves such proposed model not only leads an optimal value between the optimistic value and pessimistic＇s,but also leads a more satisfactory solution than Aboussoror＇s.Finally,a numerical experiment is given to demonstrate the feasibility of this new model.展开更多
The sufficient condition for the existence of2 π- periodic solutions of the following third- order functional differential equations with variable coefficients a(t) x (t) +bx″2 k- 1(t) +cx′2 k- 1(t) + 2 k- 1 i=1...The sufficient condition for the existence of2 π- periodic solutions of the following third- order functional differential equations with variable coefficients a(t) x (t) +bx″2 k- 1(t) +cx′2 k- 1(t) + 2 k- 1 i=1 cixi(t) +g(x(t-τ) ) =p(t) =p(t+2π) is obtained.The approach is based on the abstract continuation theorem from Mawhin and the a- priori estimate of periodic solutions展开更多
This paper concerns the existence of affine-periodic solutions for perturbed affine-periodic systems.This kind of affine-periodic solutions has the form of x(t+T)≡Qx(t) with some nonsingular matrix Q,which may be qua...This paper concerns the existence of affine-periodic solutions for perturbed affine-periodic systems.This kind of affine-periodic solutions has the form of x(t+T)≡Qx(t) with some nonsingular matrix Q,which may be quasi-periodic when Q is an orthogonal matrix. It can be even unbounded but x(t)/|x(t)| is quasi-periodic,like a helical line. for example x(t)=e^(at)(cos ωt, sin ωt), when Q is not an orthogonal matrix. The averaging method of higher order for finding affine-periodic solutions is given by topological degree.展开更多
The existence of the multiple positive periodic solutions to a delayed statedependent predator-prey system with non-monotonic functional response is considered. Using the continuation theorem based on Mawhin＇s coinci...The existence of the multiple positive periodic solutions to a delayed statedependent predator-prey system with non-monotonic functional response is considered. Using the continuation theorem based on Mawhin＇s coincidence degree, some more generalized results are obtained.展开更多
基金supported by the National Natural Science Foundation of China(1140145071171150+4 种基金71471143)the Hubei Provincial Department of Education(B2015348D20141101)the Hubei Province Key Laboratory of Systems Science in Metallurgical Process(Y201518Z201401)
文摘Partial cooperation formulation is a more viable option than optimistic＇s and pessimistic＇s to solve an ill-posed bilevel programming problem.Aboussoror＇s partial cooperation model uses a constant as a cooperation index to describe the degree of follower＇s cooperation.The constant only indicates the leader＇s expectation coefficient for the follower＇s action,not the follower＇s own willingness.To solve this situation,a new model is proposed by using the follower＇s satisfactory degree as the cooperation degree.Then,because this new cooperation degree is a function which is dependent on the leader＇s choice and decided by the follower＇s satisfactory degree,this paper proves such proposed model not only leads an optimal value between the optimistic value and pessimistic＇s,but also leads a more satisfactory solution than Aboussoror＇s.Finally,a numerical experiment is given to demonstrate the feasibility of this new model.
基金Supported by the National Natural Science Foundation of China(1 9971 0 2 6 )
文摘The sufficient condition for the existence of2 π- periodic solutions of the following third- order functional differential equations with variable coefficients a(t) x (t) +bx″2 k- 1(t) +cx′2 k- 1(t) + 2 k- 1 i=1 cixi(t) +g(x(t-τ) ) =p(t) =p(t+2π) is obtained.The approach is based on the abstract continuation theorem from Mawhin and the a- priori estimate of periodic solutions
基金supported by National Basic Research Program of China (Grant No. 2013CB834100)National Natural Science Foundation of China (Grant Nos. 11571065,11171132 and 11201173)
文摘This paper concerns the existence of affine-periodic solutions for perturbed affine-periodic systems.This kind of affine-periodic solutions has the form of x(t+T)≡Qx(t) with some nonsingular matrix Q,which may be quasi-periodic when Q is an orthogonal matrix. It can be even unbounded but x(t)/|x(t)| is quasi-periodic,like a helical line. for example x(t)=e^(at)(cos ωt, sin ωt), when Q is not an orthogonal matrix. The averaging method of higher order for finding affine-periodic solutions is given by topological degree.
基金the National Natural Science Foundation of China under Grant 10671133
文摘The existence of the multiple positive periodic solutions to a delayed statedependent predator-prey system with non-monotonic functional response is considered. Using the continuation theorem based on Mawhin＇s coincidence degree, some more generalized results are obtained.
