Fixed points of increasing operators and solutions of nonlinear impulsive integro-differential equations in Banach space
The authors study the initial value problem (IVP) of the nonlinear impulsive integro-differential equations in Banach space. \[ x'= f(t,x,Tx,Sx),\;t\neq t_i;\quad \Delta x|_{t=t_i} =I_i(x),\;i=1,2,\dots,p; \quad x(0)=x_0. \] They prove some new fixed-point theorems for increasing operators, which are also the generalization of known results. Then, they use these fixed point theorems to discuss the existence of the extremal solutions of IVP, without assuming that \(f,k,h\), and \(I_i(i=1,2,\dots,p)\) are continuous.
nonlinear impulsive integro-differential equations
scientific article; zbMATH DE number 1513362