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) = lambda a(x)f(u(x)) for x is an element of(0,1), u(0) = u(1) = u '(0) = u '(1) = 0, where lambda > 0 is a parameter, a is an element of L-1(0, 1) may change sign and f is an element of C([0, infinity), [0, infinity)). We establish some new results of existence of positive solutions to this problem if the nonlinearity f is monotone on [0, infinity). 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.