BOUNDARY-VALUE-PROBLEMS FOR NONLINEAR 4TH-ORDER EQUATIONS WITH APPLICATIONS TO NONLINEAR BEAMS

Existence results for the nonlinear differential equation y(iv) = f(t, y, y', y', y'''), 0 less-than-or-equal-to t less-than-or-equal-to 1 are given for a variety of boundary conditions and growth rate as-sumptions on the nonlinear term f. In particular, we consider assumptions on f which are analogous to those used by Bernstein for second order problems as well as essentially different integral-monotonocity conditions. The boundary conditions considered include those appropriate for a beam in equilibrium. The eistence results are based on topological transversality and the use of a priori bounds.