In his article 'Boundedness of a Class of Second-order Ordinary Differential Equations With Delay', Wen Lizhi has demonstrated the criterion of the boundedness of solutions of the equation (r(t)y’)’+a(t)y+b(...In his article 'Boundedness of a Class of Second-order Ordinary Differential Equations With Delay', Wen Lizhi has demonstrated the criterion of the boundedness of solutions of the equation (r(t)y’)’+a(t)y+b(t)f(y(t-ι(t)))=p(t) (cf. Kexue Tongbao,30(1985), 1045). In this letter, we discuss the boundedness of solutions of the secondorder nonlinear functional differential展开更多
In this paper a function called P-function is introduced. A class of neutral functional differential equations which include ones with bounded lag and unbounded lag is defined by the P-function. The basic theory is es...In this paper a function called P-function is introduced. A class of neutral functional differential equations which include ones with bounded lag and unbounded lag is defined by the P-function. The basic theory is established in space C consisting of continuous functions defined on a finite interval.展开更多
In this paper, we investigate the continuous dependence of solutions of the functional dif-ferential equation with infinite delay x'(t) = f(t, x_t) on initial functions. Endowing the phasespare a g-norm as well as...In this paper, we investigate the continuous dependence of solutions of the functional dif-ferential equation with infinite delay x'(t) = f(t, x_t) on initial functions. Endowing the phasespare a g-norm as well as a supremum norm. we show that if the equation satifies a mild fadingmemory dondition, then the continuity of f in respect to the topology induced by the supremumnorm can yield the continuity of solutions of the equation in respect to the topology induced bythe g-norm which is stronger than the ahead one.展开更多
文摘In his article 'Boundedness of a Class of Second-order Ordinary Differential Equations With Delay', Wen Lizhi has demonstrated the criterion of the boundedness of solutions of the equation (r(t)y’)’+a(t)y+b(t)f(y(t-ι(t)))=p(t) (cf. Kexue Tongbao,30(1985), 1045). In this letter, we discuss the boundedness of solutions of the secondorder nonlinear functional differential
文摘In this paper a function called P-function is introduced. A class of neutral functional differential equations which include ones with bounded lag and unbounded lag is defined by the P-function. The basic theory is established in space C consisting of continuous functions defined on a finite interval.
基金This research was supported in part by an NSF grant with number NSY-DMS-8521408. On leave from South China Normal University, Guangshou, PRC. This research was supported in part by the National Science Foundation of PRC
文摘In this paper, we investigate the continuous dependence of solutions of the functional dif-ferential equation with infinite delay x'(t) = f(t, x_t) on initial functions. Endowing the phasespare a g-norm as well as a supremum norm. we show that if the equation satifies a mild fadingmemory dondition, then the continuity of f in respect to the topology induced by the supremumnorm can yield the continuity of solutions of the equation in respect to the topology induced bythe g-norm which is stronger than the ahead one.
