We offer criteria for the existence of positive solutions for two-point right focal eigenvalue problems ( − 1 ) n − p y Δ n ( t ) = λ f ( t , y ( σ n − 1 ( t ) ) , y Δ ( σ n − 2 ( t ) ) , … , y Δ p − 1 ( σ n − p ( t ) ) ) , t ∈ [ 0 , 1 ] ∩ T , y Δ i ( 0 ) = 0 , 0 ≤ i ≤ p − 1 , y Δ i ( σ ( 1 ) ) = 0 , p ≤ i ≤ n − 1 , where λ > 0 , n ≥ 2 , 1 ≤ p ≤ n − 1 are fixed and T is a time scale.