Existence and continuation of solutions for a nonlinear Neumann problem

In this article we study the existence, continuation and bifurcation from infinity of nonconstant solutions for a nonlinear Neumann problem. We apply the Leray–Schauder degree and the degree for SO(2)SO(2)-equivariant gradient operators defined by the second author in [S. Rybicki, SO(2)SO(2)-degree for orthogonal maps and its applications to bifurcation theory, Nonlinear Anal. TMA 23 (1) (1994) 83–102].