On a Class of Inclusions in Ordered Spaces
Nguyen Bich HuyCollege of Education, Hochiminh City, Vietnam
Dao Bao DungCollege of Education, Hochiminh City, Vietnam
Nguyen Huu KhanhCollege of Sciences, Cantho City, Vietnam
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.
Cite this article
Nguyen Bich Huy, Dao Bao Dung, Nguyen Huu Khanh, On a Class of Inclusions in Ordered Spaces. Z. Anal. Anwend. 22 (2003), no. 3, pp. 543–551DOI 10.4171/ZAA/1161