Three solutions of an [formula omitted]th order three-point focal type boundary value problem

Abstract

We consider the following differential equation u ( n ) ( t ) = F ( t , u ( t ) ) , t ∈ [ 0 , 1 ] , together with the three-point focal type boundary conditions u ( j ) ( 0 ) = 0 , 0 ≤ j ≤ n − 3 , u ( n − 2 ) ( p ) = 0 , u ( n − 1 ) ( 1 ) = 0 , where 1 2 < p < 1 . By using two different fixed-point theorems, we offer criteria for the existence of three positive solutions of this problem. Examples are also included to illustrate the results obtained.