Abstract
We obtain sufficient conditions, expressed in terms of Wiener type tests involving Hausdorff or Bessel capacities, for the existence of large solutions to equations (1) −Δ p u+e u − 1 = 0 or (2) −Δ p u + u q = 0 in a bounded domain Ω when q > p − 1 > 0. We apply our results to equations (3) −Δ p u + a|∇u|q + bu s = 0, (4) Δ p u + u −γ = 0 with 1 < p ≤ 2, 1 ≤ q ≤ p, a > 0, b > 0 and q > p − 1, s ≥ p − 1, γ > 0.
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Nguyen, QH., Véron, L. Wiener Criteria for Existence of Large Solutions of Quasilinear Elliptic Equations with Absorption. Potential Anal 42, 681–697 (2015). https://doi.org/10.1007/s11118-014-9453-2
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DOI: https://doi.org/10.1007/s11118-014-9453-2