q-Lidstone polynomials and existence results for q-boundary value problems - Mansour, Zeinab; Al-Towailb, Maryam (Boundary value problems, 2017)
In this paper, we study some properties of q -Lidstone polynomials by using Green’s function of certain q -differential systems. The q -Fourier series expansions of these polynomials are given. As an application, we prove the existence of solutions for the linear q -difference equations ( − 1 ) n D q − 1 2 n y ( x ) = ϕ ( x , y ( x ) , D q − 1 y ( x ) , D q − 1 2 y ( x ) , … , D q − 1 k y ( x ) ) , subject to the boundary conditions D q − 1 2 j y ( 0 ) = β j , D q − 1 2 j y ( 1 ) = γ j ( β j , γ j ∈ C , j = 0 , 1 , … , n − 1 ) , where n ∈ N and 0 ≤ k ≤ 2 n − 1 . These results are a q -analogue of work by Agarwal and Wong of 1989.