Abdellaoui, BBouguima, SmPeral, I2013-05-152013-05-1520111120-6330https://dspace.univ-tlemcen.dz/handle/112/1891RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI , ISSN : 1120-6330, DOI : 10.4171/RLM/586, Issue : 1, Volume :22, pp. 29-50, 2011.We will consider the following obstacle problemintegral(Omega)del u del T(k)(v -u)dx + integral(Omega)h(u)vertical bar del u vertical bar(q)T(k)(v - u)dx >= integral(Omega)(g(x, u) + f)T(k)(v - u)dx,with the condition that u >= Psi a.e in Omega. Under suitable condition relating g, h and q, we show the existence of a solution for all f is an element of L(1)(Omega).The main feature is, assuming that g(x, s) is asymptotically linear as vertical bar s vertical bar -> +/-infinity and independently of the values oflim(s ->+/-infinity)g(x, s)/s,to obtain a solution for all lambda > 0 and f is an element of L(1) (Omega). In this sense we could say that the first order term break down any resonant effect.enNonlinear obstacle problemsexistence and nonexistenceregularizationresonanceArticle