Bifurcation techniques and positive solutions of discrete Lidstone boundary value problems
Abstract Let n ⩾ 1, T ⩾ n + 5 be two positive integers and T n = { n , n + 1 , … , T } . We consider the existence of solutions of the discrete Lidstone boundary value problem. ( - 1 ) n Δ 2 n u ( t - n ) = f ( t , u ( t ) , Δ 2 u ( t - 1 ) , … , Δ 2 n - 2 u ( t - n + 1 ) ) , t ∈ T n , Δ 2 i u ( n - i - 1 ) = Δ 2 i u ( T - i + 1 ) = 0 , i = 0 , 1 , … , n - 1 , where f : T n × R n → R is continuous.