WOS: 000282916600004Let T be a time scale with [a, b] subset of T. We establish criteria for existence of one or more than one positive solutions of the non-eigenvalue problem (0.1) {y Delta(4)(t) - q(t)y Delta(2) (sigma(t)) = f(t, y(t)) = f(t,y(t)), t is an element of [a, b] subset of T, y(a) = Sigma(m-2)(i=1) a(i)y(xi(i)), y(sigma(2)(b)) = Sigma(m-2)(i=1) b(i)y(xi(i)), y Delta(2)(a) = Sigma(m-2)(i=1) a(i)y Delta(2)(xi(i)), y Delta(2)(sigma(2)(b)) = Sigma(m-2)(i=1) b(i)y Delta(2)(xi(i)), where xi(i) is an element of (a, b), a(i), b(i) is an element of [0, infinity) (for i is an element of {1, 2, ... , m - 2}) are given constants. Later, we consider the existence and multiplicity of positive solutions for the eigenvalue problem y Delta(4) (t) - q(t)y Delta(2) (sigma(t)) = lambda f (t, y(t)) with the same boundary conditions. We shall also obtain criteria which lead to nonexistence of positive solutions. In both problems, we will use Krasnoselskii fixed point theorem
