EXISTENCE OF SOLUTIONS OF MIXED TWO-POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FOURTH-ORDER DIFFERENTIAL EQUATION

In this paper, the authors study the fourth-order nonlinear ordinary differential equation y((4))(t) = f (t, y(t), y'(t), y ''(t), y'''(t)), a < t < b with the mixed two-point boundary conditions c(1)y'(a) + d(1)y(b) = 0, y'(b) = 0, c(2)y ''(a) - d(2)y'''(b) = 0, y'''(a) = 0, where f : [a, b] x R-4 -> R is continuous, c(1), d(2) are nonnegative constants and d(1), c(2) are positive constants. Some new existence results are obtained by developing the upper and lower solution method and the monotone iterative technique. Some applications are also presented.