Infinitely many solutions for semilinear elliptic problems with sign-changing weight functions

摘要

In this paper, we study the elliptic problem -Δu + u = a(x)|u|~(p-2)u + b(x)|u|~(q-2)u; u ∈ H~1(R~N), where 2~* is the critical Sobolev exponent, 2 < p < q < 2~* and a or b is a sign-changing function. Under different assumptions on a and b we prove the existence of infinitely many solutions to the above problem. We also show that one of these solutions is positive.