On linear and nonlinear fourth-order eigenvalue problems with nonlocal boundary condition

We determine the principal eigenvalue of the linear problem u (4) (t) + β u ′′ (t) = [ u (t) - u ′′ (t) ],t ∈ (0,1),u (0) = u (1) = ∫ 0 1 p (s) u (s) d s,u ′′ (0) = u ′′ (1) = ∫ 0 1 q (s) u ′′ (s) d s,where 0 < β < π 2 and p,q ∈ l [ 0,1 ]. moreover,we investigate the existence of positive solutions for the corresponding nonlinear problem. the proofs of our main results are based upon the krein-rutman theorem and fixed point index theory. © 2013 dongming yan.