Summary: We use solution matching to study the uniqueness and existence of solutions for the nonlocal boundary value problem for the third-order differential equation, \[ y'''(x)= f(x, y(x))\quad\text{on }[a, c] \] satisfying \[ y(a)- \int^b_a y(x)d\alpha(x)= y_1,\;y'(b)= y_2,\;\int^c_b y(x) d\beta(x)- y)c)= y_3, \] where \[ \int^b_a y(x)d\alpha(x)\quad\text{and}\quad \int^c_b y(x)d\beta(x) \] are Riemann-Stieltjes integrals with positive measures \(d\alpha(x)\) and \(d\beta(x)\), respectively. We match solutions on \([a,b]\) with solutions on \([b,c]\). Monotonicity conditions and some growth conditions on \(f\) are imposed.