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. 29–50DOI 10.4171/RLM/586