NONLOCAL BOUNDARY VALUE PROBLEMS WITH EVEN GAPS IN BOUNDARY CONDITIONS FOR THIRD ORDER DIFFERENTIAL EQUATIONS

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)), on an interval [a, c] satisfying y(a) - integral(b)(a) y(x)d alpha(x) = y(1), y'(b) = y(2), integral(c)(b) y(x)d beta(x) - y(c) = y(3), where integral(b)(a) y(x)d alpha(x) and integral(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.