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

In this paper, we are concerned with the global bifurcation results for quasilinear elliptic problem {-div(phi(p)(del y)) = lambda a(x)phi p(y) + a(x)f(x,y,lambda) + g(x,y,lambda), in B, y = 0, on partial derivative B, where. is a parameter, f, g. C(B x R x R, R). Let B be a unit open ball of RN with a smooth boundary.B. We shall show that there are two distinct unbounded continua C-k(+) k and C-k(-), consisting of the bifurcation branch C k if f is not necessarily differentiable at the origin with respect to.p(y), and there are two distinct unbounded continua D-k(+) and D-k(-), consisting of the bifurcation branchD k if f is not necessarily differentiable at infinity with respect to.p(y). 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 In this paper, we are concerned with the global bifurcation results for quasilinear elliptic problem {-div(phi(p)(del y)) = lambda a(x)phi p(y) + a(x)f(x,y,lambda) + g(x,y,lambda), in B, y = 0, on partial derivative B, where f, g is an element of C(R, R) and g is not necessarily differentiable at the origin and infinity with respect to phi(p)(y). Furthermore, by using a comparison theorem, we also obtain a non-existence result of nodal solutions to the above problem.