Abstract
Let Omega be a smooth bounded domain in R-n;n >= 2. This paper deals with the existence and the a symptotic behavior of positive solutions of the following problems Delta u-a(x)u(alpha), alpha > 1and Delta u=a(x)e(u); with the boundary condition u broken vertical bar partial derivative Omega = +infinity The weight function a(x) is positive in C-loc(gamma) 0< gamma <1,and satisfies an appropriate assumption related to Karamata regular variation theory. Our arguments are based on the sub-super solution method.