Unilateral global interval bifurcation and one-sign solutions for Kirchhoff type problems

In this paper, we study the following Kirchhoff type problems: { - ( R ohm |del u | 2 dx )triangle u = A u 3 + g ( u , A ) , in ohm , u = 0 , on partial derivative ohm , where A is a parameter. Under some natural hypotheses on g and ohm, we establish a unilateral global bifurcation result from interval for the above problem. By applying the above result, under some suitable assumptions on nonlinearity, we shall investigate the existence of one -sign solutions for a class of Kirchhoff type problems.