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

Matching 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][a,c] for the nnth order ordinary differential equation y(n)=f(x,y,y′,…,y(n−1))y(n)=f(x,y,y′,…,y(n−1)), for n≥3n≥3, by matching solutions on [a,b][a,b] with solutions on [b,c][b,c]. In this paper, we consider a general case where the gap in boundary conditions at bb is odd. Different monotonicity conditions on ff are imposed for distinct cases that arise.