The aim of this paper is to explore the method of lower and upper solutions in order to give some existence results for equations of the formwith the Navier conditionThe main tool is the Schauder fixed point theorem.

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In this paper, we study the global behavior of positive solutions of fourth-order boundary value problems u = λf (x, u), x ∈ (0, 1), u(0) = u(1) = u (0) = u (1) = 0, where f : [0, 1] × R + → R is a continuous function with f (x, 0) < 0 in (0, 1), and λ > 0. The proof of our main results are based upon bifurcation techniques.

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