Multiplicity of positive weak solutions to subcritical singular elliptic Dirichlet problems

摘要

We study a superlinear subcritical problem at infinity of the form ?Du =a (x) u?a + f (l, x, u) in W, u = 0 on ?W, u > 0 in W, where W is a bounded domainin Rn, 0 ≤ a 2 L￥ (W) , and 0 < a < 3. Under suitable assumptions on f , we provethat there exists L > 0 such that this problem has at least one weak solution in H01 (W)if and only if l 2 [0, L] ; and also that there exists L? such that for any l 2 (0, L?), atleast two solutions exist.