GLOBAL STRUCTURE OF POSITIVE SOLUTIONS FOR SECOND ORDER DISCRETE PERIODIC BOUNDARY VALUE PROBLEM WITH INDEFINITE WEIGHT

We show the global structure of positive solutions for second order periodic boundary value problem(-Delta(2)u(t-1)=lambda a(t)g(u(t)), t is an element of NT1,u(0)=u(T),u(1)=u(T+1),where NT1={1,2,...,T},T >= 3 is an integer,lambda>0 is a parameter,g:[0,infinity)->[0,infinity)is a continuousfunction withg(0)=0 anda:NT1 -> Ris sign-changing. Depending on the behavior ofgnear0 and infinity,we obtain that there exist0< lambda 0 <=lambda 1such that above problem has at least two positive solutions for lambda>lambda 1and no solution for lambda is an element of(0,lambda 0). The proof of our main results is based upon bifurcation technique