Existence for Nonlinear Fourth-Order Two-Point Boundary Value Problems.

The present paper is devoted to the solvability of various two-point boundary value problems for the equation y (4) = f (t , y , y ′ , y ″ , y ‴) , where the nonlinearity f may be defined on a bounded set and is needed to be continuous on a suitable subset of its domain. The established existence results guarantee not just a solution to the considered boundary value problems but also guarantee the existence of monotone solutions with suitable signs and curvature. The obtained results rely on a basic existence theorem, which is a variant of a theorem due to A. Granas, R. Guenther and J. Lee. The a priori bounds necessary for the application of the basic theorem are provided by the barrier strip technique. The existence results are illustrated with examples. [ABSTRACT FROM AUTHOR]