In this article we study the quasilinear elliptic equation with absorption lower term
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,f for nonnegative solutions we prove an estimate of the form
with constant c, independent on u(x). Using this estimate we give a simple proof of the Harnack inequality.
Submitted June 14, 2017. Published April 16, 2018.
Math Subject Classifications: 35J15, 35J60, 35J62.
Key Words: Harnack inequality; quasilinear elliptic equation; Keller-Osserman type estimate; absorption lower term.
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| Kateryna Buryachenko |
Vasyl' Stus Donetsk National University
600-richa Str., 21
Vinnytsia, 21021, Ukraine
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