The authors deal with a general boundary value problem of the type: \(x'=F(t,x),T(x)=y,y\in R^ n\) where \(F(t,x)=A(t)x+f(t,x)\) and T is a continuous but not necessarily linear operator. It is shown that under suitable conditions the problem has at least one solution. The proof relies on a fixed-point theorem for condensing maps. An example of a nonlinear second order differential equation is provided.