Buryachenko, Kateryna2022-01-312022-01-312018-04-16Buryachenko, K. (2018). Harnack inequality for quasilinear elliptic equations with (p,q) growth conditions and absorption lower order term. <i>Electronic Journal of Differential Equations, 2018</i>(91), pp. 1-9.1072-6691https://hdl.handle.net/10877/15258In this article we study the quasilinear elliptic equation with absorption lower term -div (g(|∇u|) ∇u/|∇u|) + ƒ(u) = 0, u ≥ 0. Despite of the lack of comparison principle, we prove a priori estimate of Keller-Osserman type. Particularly, under some natural assumptions on the functions g, ƒ for nonnegative solutions we prove an estimate of the form ∫0u(x) ƒ(s) ds ≤ c u(x)/r g(u(x)/r), x ∈ Ω, B8r(x) ⊂ Ω, with constant c, independent on u(x). Using this estimate we give a simple proof of the Harnack inequality.Text9 pages1 file (.pdf)enAttribution 4.0 InternationalHarnack inequalityQuasilinear elliptic equationKeller-Osserman type estimateAbsorption lower termArticle