Fixed point theorems for multifunctions with applications to discontinuous operator and differential equations (Q1883075)

The authors consider ordered topological vector spaces having certain convergence properties and give conditions which ensure that certain increasing multifunctions in those ordered topological vector spaces have a maximal fixed point and/or a minimal fixed point. They also consider certain lattice-ordered reflexive Banach spaces equipped with the weak topology and having certain convergence properties and apply their results to show that a certain operator equation and a certain quasilinear discontinuous boundary value problem have maximal and minimal solutions.