设m(t)∈C[J_k,R^+](k=1,2,…,m),且满足不等式m(t)≤(L_1+L_2t)integral from n=0 to t m(s)ds+L_3t integral from n=0 to a m(s)ds+sum from 0<t_k<t M_km(t_k),其中L_i≥0(i=1,2,3),M_k≥0满足KaL_3(e~δ^((L_1+aL_2))-1)<...设m(t)∈C[J_k,R^+](k=1,2,…,m),且满足不等式m(t)≤(L_1+L_2t)integral from n=0 to t m(s)ds+L_3t integral from n=0 to a m(s)ds+sum from 0<t_k<t M_km(t_k),其中L_i≥0(i=1,2,3),M_k≥0满足KaL_3(e~δ^((L_1+aL_2))-1)<L_1+aL_2或者a(2L_1+aL_2+aKL_3)<2,这里δ=(max)/(0≤k≤m)(t_(k+1)-t_k),K=inf{d≥1:integral from n=0 to a m(s)ds≤d (min)/(0≤k≤m) integral from t_k to t_(k+1)m(s)ds}·则m(t)=0,t∈J.我们首先指出上述的下确界K不存在,然后在比较宽松的条件下,获得了Banach空间中一阶非线性脉冲积分-微分方程初值问题解的存在性定理,本质上改进和更正了现有的结果.展开更多
In this paper, by establishing a new comparison result and using the monotone iterative technique, the existence of maximal and minimal solutions of the boundary value problem for second-order impulsive differential e...In this paper, by establishing a new comparison result and using the monotone iterative technique, the existence of maximal and minimal solutions of the boundary value problem for second-order impulsive differential equation which depends on x’ in Banach space is obtained.展开更多
By developing a comparison result and using the monotone iterative technique, we obtain the existence of the minimal and the maximal solutions to an integral boundary value problem for first order impulsive integro-di...By developing a comparison result and using the monotone iterative technique, we obtain the existence of the minimal and the maximal solutions to an integral boundary value problem for first order impulsive integro-differential equations.展开更多
Under loose conditions, the existence of solutions to initial value problem are studied for second order impulsive integro-differential equation with infinite moments of impulse effect on the positive half real axis i...Under loose conditions, the existence of solutions to initial value problem are studied for second order impulsive integro-differential equation with infinite moments of impulse effect on the positive half real axis in Banach spaces. By the use of recurrence method, Tonelii sequence and the locally convex topology, the new existence theorems are achieved, which improve the related results obtained by Guo Da-jun.展开更多
文摘设m(t)∈C[J_k,R^+](k=1,2,…,m),且满足不等式m(t)≤(L_1+L_2t)integral from n=0 to t m(s)ds+L_3t integral from n=0 to a m(s)ds+sum from 0<t_k<t M_km(t_k),其中L_i≥0(i=1,2,3),M_k≥0满足KaL_3(e~δ^((L_1+aL_2))-1)<L_1+aL_2或者a(2L_1+aL_2+aKL_3)<2,这里δ=(max)/(0≤k≤m)(t_(k+1)-t_k),K=inf{d≥1:integral from n=0 to a m(s)ds≤d (min)/(0≤k≤m) integral from t_k to t_(k+1)m(s)ds}·则m(t)=0,t∈J.我们首先指出上述的下确界K不存在,然后在比较宽松的条件下,获得了Banach空间中一阶非线性脉冲积分-微分方程初值问题解的存在性定理,本质上改进和更正了现有的结果.
基金Foundation item: Science Foundation of Shanxi Province 20051009 and 2006011013.
文摘In this paper, by establishing a new comparison result and using the monotone iterative technique, the existence of maximal and minimal solutions of the boundary value problem for second-order impulsive differential equation which depends on x’ in Banach space is obtained.
基金supported by Natural Science Foundation of Hunan (No.09JJ6010)
文摘By developing a comparison result and using the monotone iterative technique, we obtain the existence of the minimal and the maximal solutions to an integral boundary value problem for first order impulsive integro-differential equations.
基金Project supported by the National Natural Science Foundation of China(Nos. 10572057 and 10251001)the Science Foundation of Nanjing University of Aeronautics and Austronautics
文摘Under loose conditions, the existence of solutions to initial value problem are studied for second order impulsive integro-differential equation with infinite moments of impulse effect on the positive half real axis in Banach spaces. By the use of recurrence method, Tonelii sequence and the locally convex topology, the new existence theorems are achieved, which improve the related results obtained by Guo Da-jun.
