Solutions and Positive Solutions of a Class of Semilinear Fourth-Order Elastic Beam Equations

Abstract:

      The existence of the solutions and positive solutions is studied for a class of fourth-order two-point boundary value problems with all order derivatives. In the mechanics, the class of problems describes the deformations of the elastic beam, of which an end is simply supported and the other is clamped by sliding clamps. The results show that the class of problems has at least one solution or positive solution provided the ``maximal height" of nonlinear term is appropriate on a bounded set of its domain.