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Zeitschrift für Analysis und ihre Anwendungen


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Volume 22, Issue 3, 2003, pp. 543–551
DOI: 10.4171/ZAA/1161

Published online: 2003-09-30

On a Class of Inclusions in Ordered Spaces

Nguyen Bich Huy[1], Dao Bao Dung[2] and Nguyen Huu Khanh[3]

(1) College of Education, Hochiminh City, Vietnam
(2) College of Education, Hochiminh City, Vietnam
(3) College 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.

Keywords: Increasing multi-valued operators, inclusions, ordered spaces, implicit elliptic equations

Huy Nguyen Bich, Dung Dao Bao, Khanh Nguyen Huu: On a Class of Inclusions in Ordered Spaces. Z. Anal. Anwend. 22 (2003), 543-551. doi: 10.4171/ZAA/1161