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
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.
