The nonlocal boundary value problem, with p -Laplacian of the form ( Φ p ( u ▵ ) ) ▵ ( t ) + h ( t ) f ( t , u ( t ) ) = 0 ,   t ∈ [ t 1 , t m ) T ,   u ▵ ( t 1 ) − ∑ j = 1 n θ j u ▵ ( η j ) − ∑ i = 1 m − 2 ϵ i u ( ξ i ) = 0 ,   u ▵ ( t m ) = 0 , has been considered. Two existence criteria of at least one and three positive solutions are presented. The first one is based on the Four functionals fixed point theorem in the work of R. Avery et al. (2008), and the second one is based on the Five functionals fixed point theorem. Meanwhile an example is worked out to illustrate the main result.