Existence, uniqueness and data dependence for the solution to a boundary value problem with deviating argument (Q2755030)

Consider the scalar second-order delay differential equation NEWLINE\[NEWLINE y''(x)=f(x,y(x),y(\lambda x)) NEWLINE\]NEWLINE on the interval \([a,b]\) with \(0<a<b\), \(\lambda\in(0,1)\), \(\lambda b\geq a\), \(f\in C([0,b]\times\mathbb{R}\times\mathbb{R},\mathbb{R})\). The author provides interesting results on the existence, uniqueness and data dependence of the solutions of the above equation satisfying the boundary conditions \(y|_{[0,a]}=0\), \(y(b)=0\). The basic technical tool is Maia's fixed-point theorem.