On three-point boundary value problems associated with third order differential equations

Abstract

INTRODUCTION IN THIS paper we shall be concerned with the existence and uniqueness of solutions to three point boundary value problems associated with the differential equation y”’ = f(x, Y, Y’S Y”), (1.1) where f(x, y, z, w) is assumed to be continuous on a subset of R4. Initial-value problems associated with (1.1) exist, and are unique in the interval [x1, x,]. A monotonicity restriction on f(x, y, z, w) ensures that the following boundary value problems Y “’ = J-(x, Y, Y’, Y”), y(xJ = y, ; y(xJ = y,; y(‘)(x,) = m (i = 1,2), (12i) Y”’ = J-(x, Y, Y', Y), y(x)=y * y”)(x)=m2 2’ 2 9 Y(x,) = Y, (i = 421, (le3i)