Global bifurcation for N-dimensional p-Laplacian problem and its applications

Abstract

In this paper, we are concerned with the global bifurcation results for quasilinear elliptic problem where λ is a parameter, . Let B be a unit open ball of with a smooth boundary . We shall show that there are two distinct unbounded continua and , consisting of the bifurcation branch if f is not necessarily differentiable at the origin with respect to , and there are two distinct unbounded continua and , consisting of the bifurcation branch if f is not necessarily differentiable at infinity with respect to . As the applications of the above result, we shall prove more details about the existence and multiplicity results of sign-changing solutions for the elliptic problem where and g is not necessarily differentiable at the origin and infinity with respect to . Furthermore, by using a comparison theorem, we also obtain a non-existence result of nodal solutions to the above problem.