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Zeitschrift für Analysis und ihre Anwendungen


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Volume 21, Issue 2, 2002, pp. 371–380
DOI: 10.4171/ZAA/1083

Published online: 2002-06-30

Extremal Solutions for a Class of Unilateral Problems

Nguyen Bich Huy[1], Nguyen Duy Thanh[2] and Tran Dinh Thanh[3]

(1) College of Education, Hochiminh City, Vietnam
(2) College of Education, Hochiminh City, Vietnam
(3) College of Medicine and Pharmacy, Hochiminh City, Vietnam

We apply a fixed point theorem for increasing operators in ordered Banach spaces to prove the existence of extremal (i.e. maximal or minimal) solutions for the variational inequality $\langle Av, w – v\rangle ≥ \int _\Omega f(x, v)(w–v)dx$ where $A$ is the $p$-Laplacian and $f(x,u) = F(x,u,u)$ with $F(x,u,v)$ being a function, non-decreasing in $u$ and non-increasing in $v$.

Keywords: Fixed points, increasing operators, ordered spaces, extremal solutions, variational inequalities, unilateral problems

Huy Nguyen Bich, Thanh Nguyen Duy, Thanh Tran Dinh: Extremal Solutions for a Class of Unilateral Problems. Z. Anal. Anwend. 21 (2002), 371-380. doi: 10.4171/ZAA/1083