Global bifurcation of positive and negative solutions from infinity in some quasi-linear elliptic problems with sign-chining weight

In this paper we consider the nonlinear eigenvalue problem for elliptic partial differential equations with a sign-chaining weight function and study the global bifurcation from infinity of solutions to this problem. We prove the existence of two pairs of global continua emanating from the asymptotic bifurcation points corresponding to the principal eigenvalues of the linearized problem and contained in the classes of positive and negative functions.