Abstract
We consider the general two-point boundary value problem for third order nonlinear differential equation on time scales,
y(Delta Delta Delta()t) + lambda f(t, y, y,(Delta) , y(Delta Delta)) = 0, t epsilon [a, b]
subject to the boundary conditions
alpha 11y(a) - alpha 12y(b) = 0 alpha 21y(Delta)(a) - alpha 22y(Delta)(b) = 0 alpha 31y(Delta Delta)(a) - a32y(Delta Delta)(sigma(b)) = 0
where the coefficients alpha 1i, alpha 2i, alpha 3i, i = 1, 2 are real positive constants. Values of the parameter. are determined for which boundary value problem has positive solution by utilizing a fixed point theorem on cone.