An obstacle problem with gradient term and asymptotically linear reaction

  • Boumediene Abdellaoui

    Université Aboubekr Belkaïd, Tlemcen, Algeria
  • Sidi Mohamed Bouguima

    Université Aboubekr Belkaïd, Tlemcen, Algeria
  • Ireneo Peral

    Universidad Autónoma de Madrid, Spain

Abstract

We will consider the following obstacle problem

with the condition that a.e in Under suitable condition relating , and , we show the existence of a solution for all .

The main feature is, assuming that is asymptotically linear as and independently of the values of to obtain a solution for all and . In this sense we could say that the first order term break down any resonant effect.

Cite this article

Boumediene Abdellaoui, Sidi Mohamed Bouguima, Ireneo Peral, An obstacle problem with gradient term and asymptotically linear reaction. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 22 (2011), no. 1, pp. 29–50

DOI 10.4171/RLM/586