Monotone positive solution of fourth order boundary value problem with mixed integral and multi-point boundary conditions

In this paper, we investigate the existence of monotone positive solutions for a fourth order boundary value problem with dependence on the derivative in nonlinearity under integral and multi-point boundary conditions. By applying the fixed point theorem in a cone, some criteria on the existence of positive solutions are acquired. These criteria are given by explicit conditions which are generally weaker than those derived by using the classical norm-type expansion and compression theorem. As applications, three examples are presented to illustrate the validity of our mains results.