Bifurcation of obstacle problems with inclusions follow from degree results for variational inequalities

Abstract

It is shown that every result about a local degree and thus about bifurcation for variational inequalities (which is usually an obstacle problem) leads to a corresponding result for a problem in which the obstacle is modeled by inclusions instead of inequalities. Using recent results about variational inequalities, we obtain in particular bifurcation of stationary spatially nonhomogeneous solutions of a reaction-diffusion system with only Neumann conditions and obstacles modeled by inclusions, and results for an elliptic equation with inclusions about bifurcation strictly between certain eigenvalues and also bifurcation at eigenvalues without multiplicity assumptions.