Bifurcation for the solutions of equations involving set valued mappings (Q1068350)

We prove bifurcation results for set valued equations of the form \(x\in \mu Ax+R(x,\mu)\), where \(A: X\to X\) is compact linear and R is a compact, convex valued compact mapping which is \(o(\| x\|)\) uniformly in \(\mu\) in compact intervals and some bounded open neighbourhood of zero in X. Our results extend the theorem of Krasnosel'skii and Rabinowitz concerning bifurcation from \((0,\mu_ 0)\), where \(\mu_ 0\) is a characteristic value of A of odd multiplicity. The results are applied to a two point boundary value problem.