This paper studies the nonlinear delay impulsive respiratory dynamics model. The model describes the sudden changes of the concentration of CO2 in the blood of the mammal. It is proved that the model has a unique posi...This paper studies the nonlinear delay impulsive respiratory dynamics model. The model describes the sudden changes of the concentration of CO2 in the blood of the mammal. It is proved that the model has a unique positive periodic solution. Somesufficient conditions for oscillation of all positive solutions about the positive periodic solution are established and also some sufficient conditions for the global attractivityof the periodic solution are obtained.展开更多
Some new oscillation criteria for nonlinear delay difference equation with damping △^2xn＋pn△xn＋F（n,x（n-τ,△x（n-σ）=0,n=0,1,2,…,（＊）are given. Our results partially solve the open problem posed in [Math. Bo...Some new oscillation criteria for nonlinear delay difference equation with damping △^2xn＋pn△xn＋F（n,x（n-τ,△x（n-σ）=0,n=0,1,2,…,（＊）are given. Our results partially solve the open problem posed in [Math. Bohemica, 125 （2000）, 421- 430]. Also, we will establish some new oscillation criteria for special cases of （＊）, which improve some of the well-known results in the literature.展开更多
In this paper we establish some new dynamic inequalities on time scales which contain in particular generalizations of integral and discrete inequalities due to Hardy, Littlewood, Polya, D＇Apuzzo, Sbordone and Popoli...In this paper we establish some new dynamic inequalities on time scales which contain in particular generalizations of integral and discrete inequalities due to Hardy, Littlewood, Polya, D＇Apuzzo, Sbordone and Popoli. We also apply these inequalities to prove a higher integrability theorem for decreasing functions on time scales.展开更多
文摘This paper studies the nonlinear delay impulsive respiratory dynamics model. The model describes the sudden changes of the concentration of CO2 in the blood of the mammal. It is proved that the model has a unique positive periodic solution. Somesufficient conditions for oscillation of all positive solutions about the positive periodic solution are established and also some sufficient conditions for the global attractivityof the periodic solution are obtained.
文摘Some new oscillation criteria for nonlinear delay difference equation with damping △^2xn＋pn△xn＋F（n,x（n-τ,△x（n-σ）=0,n=0,1,2,…,（＊）are given. Our results partially solve the open problem posed in [Math. Bohemica, 125 （2000）, 421- 430]. Also, we will establish some new oscillation criteria for special cases of （＊）, which improve some of the well-known results in the literature.
文摘In this paper we establish some new dynamic inequalities on time scales which contain in particular generalizations of integral and discrete inequalities due to Hardy, Littlewood, Polya, D＇Apuzzo, Sbordone and Popoli. We also apply these inequalities to prove a higher integrability theorem for decreasing functions on time scales.
