Neumann Boundary Value Problems for Impulsive Differential Inclusions

where F : [0, 1]×R → P(R) is a compact valued multivalued map, P(R) is the family of all subsets of R, k ∈ (0, π 2 ), 0 < t1 < t2 < . . . < tm < 1, Ik ∈ C(R,R) (k = 1, 2, . . . , m), ∆x|t=tk = x(t + k )− x(t − k ), x(t + k ) and x(t − k ) represent the right and left limits of x(t) at t = tk respectively, k = 1, 2, . . . , m. In the literature there are few papers dealing with the existence of solutions for Neumann boundary value problems; see [15], [16] and the references therein. Recently in [14], the authors studied Neumann boundary value problems with impulse actions.