On a problem for a system of two the second order differential equations via the theory of vector fields - Yermachenko, Inara; Sadyrbaev, Felix (Nonlinear Analysis: Modelling and Control, 2015)
We consider Dirichlet boundary value problem for systems of two second-order differential equations with nonlinear continuous and bounded functions in right-hand sides. We prove the existence of a nontrivial solution to the problem comparing behaviors of solutions of auxiliary Cauchy problems at zero solution and at infinity.