On a problem for a system of two the second order differential equations via the theory of vector fields

Abstract

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.

Keywords

• multiple solutions
• Dirichlet boundary value problem
• planar vector field
• critical points
• rotation of a vector field
• winding number