JournalszaaVol. 21, No. 2pp. 371–380

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
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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 Av,wvΩf(x,v)(wv)dx\langle Av, w – v\rangle ≥ \int _\Omega f(x, v)(w–v)dx where AA is the pp-Laplacian and f(x,u)=F(x,u,u)f(x,u) = F(x,u,u) with F(x,u,v)F(x,u,v) being a function, non-decreasing in uu and non-increasing in vv.

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