This paper is devoted to global static bifurcation theory for a class of degenerateboundary value problems for nonlinear second-order elliptic differential operators which includes as particular cases the Dirichlet and Neumann problems. In the previous paper  we treated the asymptotic linear case, for example, such nonlinear terms as $u^p$, $p > 1$, near $u = 0$ but $u + 1/u$ near $u = +\infty$. The purpose of this paper is to study the asymptotic nonlinear case, for example, such nonlinear terms as $u^p$ also near $u = +\infty$. First we prove a general existence and uniqueness theorem of positive solutions for our nonlinear boundary value problems, by using the super-subsolution method, and then we study in great detail the asymptotic nonlinear case.
"Bifurcation for nonlinear elliptic boundary value problems. III.." Adv. Differential Equations 1 (4) 709 - 727, 1996.