Harnack’s Inequality for Quasilinear Elliptic Equations with Singular Absorption Term

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Abstract

In this article we study nonnegative solutions of quasilinear equation model of which is
$$-\triangle_{p} u+V(x) f(u)= h(x)|\nabla u|^{p-1}+g(x), \,\,\,\, p>1.$$
Under the natural assumptions on the functions f, V, h and g we prove the Harnack inequality with constant independent of the solution. In the case g(x) ≡ V (x) we obtain an analogue of the well known Kilpeläinen-Malý sub-bound.

Keywords

Quasilinear elliptic equations Singular absorption term Harnack’s inequality 

Mathematics Subject Classification (2010)

35B09 35B40 35B45 35B65 

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Notes

Acknowledgements

This work is supported by grant of Ministry of Education and Science of Ukraine (grant number is 0118U003138).

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Applied Mathematics and Mechanics of NAS of UkraineSlovjansjkUkraine
  2. 2.Vasyl’ Stus Donetsk National UniversityVinnytsiaUkraine

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