Positive solutions of fourth-order boundary value problems with two parameters

In this paper the existence results of positive solutions are obtained for fourth-order boundary value problem u(4) + βu − αu = f (t,u), 0 < t <1, u(0) = u(1) = u (0) = u (1) = 0, where f : [0, 1] × R+ → R+ is continuous, α,β ∈ R and satisfy β < 2π2, α −β2/4, α/π4 + β/π2 < 1.  2003 Elsevier Science (USA). All rights reserved