研究了以下一类拟线性分数阶高阶脉冲微分方程边值问题{Dq 0+y(t)=A(t,y)y(t)+f(t,y(t),Фy(t),ψy(t)), t∈[0,1]q∈(n-1,n], y(i)(0)=0,△y(i)}t=tk=0,1≤i≤n-2,k=1,2,…,p, △y|t=tk=Ik(y(tk)),△y(n-1)|t=tk=Jk(y(tk)),k=1,2,…,p, y(0)=yo+g(y),y(n-1)(1)=y1+ m-2∑j=1 bjy(n-1)(ξj)解的存在性。通过定义一个压缩映射并利用Banach不动点定理和Krasnoselskii’s不动点定理,得到了边值问题存在唯一解和至少存在一个解的充分条件,最后分别给出一个例子来验证主要结果。
The existence of solutions for high-order impulsive boundary value problem of Caputo fractional differential equation in the form {Dq 0+y(t)=A(t,y)y(t)+f(t,y(t),Фy(t),ψy(t)), t∈[0,1]q∈(n-1,n], y(i)(0)=0,△y(i)}t=tk=0,1≤i≤n-2,k=1,2,…,p, △y|t=tk=Ik(y(tk)),△y(n-1)|t=tk=Jk(y(tk)),k=1,2,…,p, y(0)=yo+g(y),y(n-1)(1)=y1+ m-2∑j=1 bjy(n-1)(ξj)is studied. By defining a contraction mapping and using the fixed point theorems, some sufficient condi- tions for the existence of one unique solution and at least a solution are established. Further, two exam- ples are presented to illustrate the main results respectively.