On a Class of Inclusions in Ordered Spaces

Abstract

Let W be a non-empty set, X an ordered topological space, L from W to X a single-valued operator and N a set-valued operator assigning to each element of W a nonempty subset of X. Under approximate assumptions on the monotonicity of L and N we prove existence results for inclusions of the form Lx in Nx. An application of the obtained results to implicit elliptic equations of the form Lu = f(x, u, Lu) is given.