Affiliation:
1. School of Mathematical Sciences, Shandong Normal University, Ji'nan, Shandong 250014, China
Abstract
This paper is devoted to investigating the eigenvalue problems of a class of nonlinear impulsive singular boundary value problem in Banach spaces:μx′′+f(t,x)=0,t∈(0,1),t≠ti;Δx|t=ti=αix(ti-0),i=1,2,…,k;ax(0)-bx′(0)=θ;cx(1)+dx′(1)=θ,whereθdenotes the zero element of Banach space,Δx|t=ti=x(ti+0)-x(ti-0),αi>-1,a,b,c,d∈R+,γ=ac+ad+bc>0,μis a parameter, andf(t,x)may be singular att=0,1andx=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.
Funder
National Natural Science Foundation of China