Abstract
We consider the forced problem −Δpu − V(x)∣u∣p−2u = f(x), where Δp is the p-Laplacian (1 < p < ∞) in a domain Ω ⊂ ℝN, V ≥ 0 and QV(u)≔ ∫Ω ∣∇u∣pdx − ∫ΩV∣u∣pdx satisfies the condition (A) below. We show that this problem has a solution for all f in a suitable space of distributions. Then we apply this result to some classes of functions V which in particular include the Hardy potential (1.5) and the potential V(x)= λ1,p(Ω), where λ1,p(Ω) is the Poincare constant on an infinite strip.
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