Zeitschrift für Analysis und ihre Anwendungen 22 (2003), No. 3, 543--551
Copyright Heldermann Verlag 2003
On a Class of Inclusions in Ordered Spaces
Nguyen Bich Huy
Dept. of Mathematics, College of Education, 280 An Duong Vuong, Ho Chi Minh City, Vietnam
Dao Bao Dung
Dept. of Mathematics, College of Education, 280 An Duong Vuong, Ho Chi Minh City, Vietnam
Nguyen Huu Khanh
Dept. of Mathematics, College of Sciences, Cantho University, 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.
Keywords: Increasing multi-valued operators, inclusions, ordered spaces, implicit elliptic equations.
MSC: 35J65; 47H05, 47H07, 47H10
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