Positive solutions of some nonlocal fourth-order boundary value problem

By the use of the Krasnosel’skii’s fixed point theorem, the existence of one or two positive solutions for the nonlocal fourth-order boundary value problemu(4)(t)+βu″(t)=λf(t,u(t),u″(t)),00,f∈C([0,1]×[0,∞)×(-∞,0],[0,∞))p,q∈L[0,1],λ>0,f∈C([0,1]×[0,∞)×(-∞,0],[0,∞)).