四川师范大学学报（自然科学版）2017，Vol.40Issue(1)：45-50,6.DOI:10.3969/j.issn.1001-8395.2017.01.007
Banach空间含导数项的二阶脉冲微分方程的解
The Solutions for Second Order Impulsive Differential Equationswith Dependence on the Derivative Terms in Banach Spaces
摘要
Abstract
In this paper,we consider the existence and uniqueness solutions for second order impulsive differential equations with dependence on the first order derivative{-u″(t)=f(t,u(t),u′(t)),t≠ tk,t∈ J=,-Δu′|t=tk=Ik(u(tk),u′(tk)),k=1,2,…,m,u(0)=θ,u(1)=θ in Banach spaces,where,f∈ C(J× E×E,E),Ik∈ C(E×E,E),k=1,2,…,m.By choosing proper working space and equivalent norm,while the nonlinear term f(t,x,y) and Ik(x,y) satisfy more general non-compactness measure conditions,we obtain the existence results of solutions and positive solutions combining with the estimation skills of the non-compactness measure and the Sadovskii fixed-point theorem.Besides,we discuss the uniqueness of the solutions of this boundary value problem.关键词
Banach空间/非紧性测度/凝聚映射/不动点定理Key words
Banach space/non-compactness measure/condensing mapping/fixed-point theorem分类
数理科学引用本文复制引用
尚亚亚,史静文,李永祥..Banach空间含导数项的二阶脉冲微分方程的解[J].四川师范大学学报（自然科学版）,2017,40(1):45-50,6.基金项目
国家自然科学基金(11261053)和甘肃省自然科学基金(1208R-JZA129) （11261053）
