On the solvability of a cantilever-type boundary value problem by using the mixed monotone operator

Abstract

In the present paper, by using the mixed monotone operator method we prove the existence and uniqueness of positive solution to the following cantilever-type boundary value problem {u(4)(t)=f(t,u(t),u(αt))+g(t,u(t)),0<t<1,α∈(0,1),u(0)=u′(0)=u′′(1)=u′′′(1)=0. Moreover, in order to illustrate the results we present an example.