Solvability of boundary value problems for second order impulsive differential equations on whole line with a non-Carathédory nonlinearity

Abstract

We study a class of boundary value problems of the impulsive differential equations on whole lines with a non-Carathéodory nonlinearity. Sufficient conditions to guarantee the existence of solutions are established. A new Banach function space X and its relatively compact property of subset of X is proved. An example is given to illustrate the main results.

Keywords

• second order impulsive differential equation
• boundary value problem
• non-Carathéodory nonlinearity
• fixed point theorem