Abstract
We consider the problem
−div(|∇u|p−2∇u)=a(x)(um+λun), x∈ℝN, N≥3, where 0<m<p−1<n,a(x)≥0, a(x) is not identically zero. Under the condition that a(x) satisfies (H), we show that there exists
λ0>0 such that the above-mentioned equation admits at least one solution for all λ∈(0,λ0). This extends the results of Laplace
equation to the case of p-Laplace equation.