Multiple nontrivial solutions for a class of semilinear polyharmonic equations

In this paper, we are concerned with the following problem: where Ω is a bounded domain in ℝN with N ≥ 2k+1, 1 < q < 2, λ > 0, f, g are continuous functions on Ω which are somewhere positive but which may change sign on Ω. is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the existence of multiple nontrivial solutions to this equation is verified.