On the existence of solutions for a class of nonlinear fully fourth-order differential systems

This paper discusses the existence of solutions to fourth order nonlinear boundary value problem involving systems of differential equations and two point boundary conditions. The nonlinearity f ∈ C ([0,1] × Rn+ × Rn × Rn × Rn, Rn)considered in this paper includes derivatives up to order three. Using recent fixed point results for the sum of two operators, we impose a growth condition on f to establish a new existence criteria that ensure the existence of at least one and the existence of at least two nonnegative solutions.