Unique solutions of systems of second-order nonlinear two-point boundary- value problems
This paper develops theorems to guarantee the unique existence of systems of boundary value ordinary differential equations of the form: (1) \(\vec y''+\vec f(t,\vec y,\vec y')=0\) with \(\vec y(a)=\vec A\) and \(\vec y(b)=\vec B\) and \(\vec y=(y_ 1,y_ 2,...,y_ n)^ T.\) A Green's function is defined for this system. Then using the contraction mapping theorem on C[a,b] with norm \(\| v\| =\max_{1\leq i\leq n}\{\max_{[a,b]}| v_ i(t)| \}\) conditions are given to show unique existence of solutions of (1).
scientific article; zbMATH DE number 3853511
scientific article