# Extremal Solutions for a Class of Unilateral Problems

### Nguyen Bich Huy

College of Education, Hochiminh City, Vietnam### Nguyen Duy Thanh

College of Education, Hochiminh City, Vietnam### Tran Dinh Thanh

College of Medicine and Pharmacy, Hochiminh City, Vietnam

## Abstract

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 $v$.

## Cite this article

Nguyen Bich Huy, Nguyen Duy Thanh, Tran Dinh Thanh, Extremal Solutions for a Class of Unilateral Problems. Z. Anal. Anwend. 21 (2002), no. 2, pp. 371–380

DOI 10.4171/ZAA/1083