Eigenvalues of a class of singular boundary value problems of impulsive differential equations in banach spaces

This paper is devoted to investigating the eigenvalue problems of a class of nonlinear impulsive singular boundary value problem in banach spaces: x ′′ + f (t,x) = 0,t ∈ (0,1),t ≠ t i; δ x | t = t i = α i x (t i - 0),i = 1,2,.,k; a x (0) - b x ′ (0) = θ; c x (1) + d x ′ (1) = θ,where θ denotes the zero element of banach space,δ x | t = t i = x (t i + 0) - x (t i - 0),α i > - 1,a,b,c,d ∈ r +,γ = a c + a d + b c > 0,is a parameter,and f (t,x) may be singular at t = 0,1 and x = θ. the arguments are mainly based upon the theory of fixed point index,measure of noncompactness,and the special cone,which is constructed to overcome the singularity. © 2014 daliang zhao and yansheng liu.