Abstract: In the paper, by using the variational methods, the authors consider the solvability ofthe equation -△p^u=λ a(x)(u^{+})^q-1-μ a(x)(u^-)^q-1+f(x,u), u∈W₀^1,p(Ω),
(Ω) in the case of p≠ q, where Ω is a bounded domain in R^N(N≥ 3),
the weight function (x)∈ L^r(Ω), (r≥Np/Np-Nq+pq) with a(x)>0, a.e.in Ω, and f satisfies some conditions.

Key words: p-Laplacian, Eigenvalue problems, Variational methods