Positive Solutions for Fourth-Order Equations with a Sign-Changing Weight and Clamped Beam Boundary Conditions

In this paper, we are concerned with the existence of positive solutions for nonlinear fourth-order equation with clamped beam boundary conditions u (x) = λa(x) f (u(x)) for x ∈ (0, 1),u(0) = u(1) = u (0) = u (1) = 0, where λ 0 is a parameter, a ∈ L1(0, 1) may change sign and f ∈C([0,∞), [0,∞)). We establish some new results of existence of positive solutions to this problem if the nonlinearity f is monotone on [0,∞). The proofs of our main results are based upon a monotone iteration technique and the Schauder’s fixed point theorem. Finally, an example is presented to illustrate the application of our main results.