A note on boundary conditions for nonlinear operators (Q999248)

The authors start by recalling a number of well-known results and properties. Among them are the properties of the fixed point index associated to some bounded open subset inside a real Banach space and to some special map from the closure of that open set to the Banach space itself. They prove that the fixed point index vanishes under some boundary behavior assumptions on the special map. Finally, the obtained theorems are combined with some properties of the fixed point index to get eigenvalue and fixed point results under similar boundary behavior assumptions on the involved map.