Advanced Search

This paper is concerned with the existence of mild solutions for impulsive semilinear differential equations with nonlocal conditions. Using the technique of measures of noncompactness in Banach and Fréchet spaces of piecewise continuous functions, existence results are obtained both on bounded and unbounded intervals, when the impulsive functions and the nonlocal item are not compact in the space of piecewise continuous functions but they are continuous and Lipschitzian with respect to some measure...

We show that ${\omega }_0\left(X\right)={lim}_{T\to \infty }{lim}_{\epsilon \to 0}{\omega }^T(X,\epsilon )$ is a measure of noncompactness defined on some subsets of the space $C\left({ℝ}^{+}\right)=\{x:{ℝ}^{+}\to ℝ,x\text{continuous}\}$ furnished with the distance defined by the family of seminorms ${\left|x\right|}_n$. Moreover, using a technique associated with the measures of noncompactness, we prove the existence of solutions of a quadratic Urysohn integral equation on an unbounded interval. This measure allows to obtain theorems on the existence of solutions of a integral equations on an unbounded interval under a weaker assumptions then the assumptions of theorems...