Calculation of degree and global bifurcation for variational inequalities with nonsymmetric operators in Banach spaces

Abstract

In order to prove global bifurcation for variational inequalities, it is useful to know local mapping degrees for certain maps associated to the inequalities. Some methods are provided to calculate these degrees. In contrast to existing results, no symmetry on the derivatives needs to be assumed to apply these methods. In fact, it is also shown that the whole approach is possible even in the setting of Banach spaces and for noncompact operators with only positively homogeneous “derivatives”.