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: mu x(11) + f (t,x) = 0, t is an element of ( 0, 1), t not equal t ; Delta xl(t=t1) = alpha(1)x(t1 - 0), i = 1,2,...,k; ax(0) - bx(1)(0) = theta; cx(1) + dx(1)(1) = theta , where theta denotes the zero element of Banach space, Delta xl(t=t1) = alpha(1)x(t(i) + 0) - x(t(i) - 0), alpha(1) > -1,a,b,c,d is an element of R+, is a parameter, and.. (..,..) may be singular at.. = 0,1 and.. =... 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.