Abstract: By using the fixed point theorem of ksetcontraction mapping and a new estimation of the measure of noncompactness, we proved the existence of the solution for the initial value problem of ordinary differential equations with noninstantaneous impulses, and then obtained the existence of the solution for the initial value problem of ordinary differential equations with noninstantaneous impulses under the assumption that the nonlinear term satisfied some weaker growth condition and noncompactness measure condition, and the noninstantaneous impulsive functions satisfied some Lipschitz conditions.

Key words: Banach space, measure of noncompactness, ksetcontraction mapping, ordinary differential equation with noninstantaneous impulse