BVP’s with odd differences of gaps in boundary conditions for nth order ODE’s by matching solutions

AbstractMatching of solutions of boundary value problems plays an important role in interface problems. We are concerned with the existence and uniqueness of solutions to boundary value problems on an interval [a,c] for the nth order ordinary differential equation y(n)=f(x,y,y′,…,y(n−1)), for n≥3, by matching solutions on [a,b] with solutions on [b,c]. In this paper, we consider a general case where the gap in boundary conditions at b is odd. Different monotonicity conditions on f are imposed for distinct cases that arise