New results and applications on the existence results for nonlinear coupled systems

Abstract In this manuscript, we study a certain classical second-order fully nonlinear coupled system with generalized boundary conditions satisfying the monotone assumptions. Our new results unify existence criteria of linear and value problems (BVPs) that have been previously studied on case-by-case basis; for example, Dirichlet Neumann are special cases. The common feature is solution each BVPs lies in sector defined by well-ordered lower upper solutions. tools use solutions approach along some fixed point theory. By means approach, considered logically modified to problems, known as BVPs. leads original our case, only require Nagumo condition get priori bound derivatives function. Further, extend presented (Franco et al. Extr. Math. 18(2):153–160, 2003; Franco Appl. Comput. 153:793–802, 2004; O’Regan Arch. Inequal. 1:423–430, Asif Bound. Value Probl. 2015:134, 2015). Finally, an application, consider mass-spring model.