(untitled) (Journal of Partial Differential Equations, 1991)
Let &#937 be a bounded domain in R^4(n &#8805 4) with smooth boundary &#8706&#937. We discuss the existence of nontrivial solutions of the Dirichlet problem - &#916u = a(x) |u|^4/(a-2)u + &#955u + g(x, u), x &#8712 &#937 u = 0, x &#8712 &#8706&#937 where a(x) is a smooth function which is nonnegative on &#937 and positive somewhere, &#955> 0 and &#955 &#8713 &#963(-&#916). We weaken the conditions on a(x) that are generally assumed in other papers dealing with this problem.