POSITIVE SOLUTIONS FOR NONLINEAR m-POINT BVP WITH SIGN CHANGING NONLINEARITY ON TIME SCALES

In this paper, by using fixed point theorems in cones, the existence of positive solutions is considered for nonlinear m-point boundary value problem for the following second-order dynamic equations on time scales uΔ∇ (t) + a(t)f(t; u(t)) = 0; t 2 (0; T); u(0) uΔ(0) = 0; u(T) = mΣ−2 i=1 aiu( i); m 3; where a(t) 2 Cld((0; T); [0;+1)), f 2 C([0; T] 『 [0;+1); ( 1;+1)); the nonlinear term f is allowed to change sign. We obtain several existence theorems of positive solutions for the above boundary value problems. In particular, our criteria generalize and improve some known results [15] and the obtained conditions are different from related literature [14]. As an application, an example to demonstrate our results is given.