Fixed point problem associated with state-dependent impulsive boundary value problems

Abstract

The paper investigates a fixed point problem in the space (W 1,∞ ([a, b]; R n )) p+1 which is connected to boundary value problems with state-dependent impulses of the formHere, the impulse instants τ i are determined as solutions of the equations Provided the data functions f and J i are bounded, transversality conditions which guarantee that this fixed point problem is solvable are presented. As a result it is possible to realize the construction of a solution of the above impulsive problem.