Multiple positive solutions for imageth-order image-point boundary value problems with all derivatives Original Research Article

We investigate the existence of positive solutions for the boundary value problem View the MathML sourceu(n)(t)+f(t,u(t),u′(t),…,u(n−2)(t),u(n−1)(t))=0,00(i=1,2,…,m−2),0<∑i=1m−2ki<1. We give at first the associated Green’s function and some of its properties. Then, imposing growth conditions on ff, we obtain the existence of at least three positive solutions for the boundary value problem by using the five-functional-fixed-point theorem. Finally, we give an example to demonstrate our result.