Existence of solutions to second order ordinary differential equations having finite limits at +/- infinity

In this article, we study the boundary-value problem $$ ddot{x}=f(t,x,dot{x}), quad x(-infty )=x(+infty), quad dot{x}(-infty) = dot{x}(+infty ),. $$ Under adequate hypotheses and using the Bohnenblust-Karlin fixed point theorem for multivalued mappings, we establish the existence of solutions.