On existence and stability of solutions to semi-homogeneous boundary value problems (Q1910301)

Consider boundary value problems of the form \[ dx/dt= f(t,x)+ g(t,x), \quad Mx(0)+Nx(T)=0, \tag{*} \] with \(x\in\mathbb{R}^n\), \(M\) and \(N\) are matrices. The authors derive conditions such that (*) has at least one solution. The proofs are based on fixed point arguments.