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Existence of positive solutions for nonlocal p(x)-Kirchhoff elliptic systems

  • Salah Boulaaras EMAIL logo , Rafik Guefaifia and Khaled Zennir
Published/Copyright: January 18, 2018

Abstract

In this article, we discuss the existence of positive solutions by using sub-super solutions concepts of the following p(x)-Kirchhoff system:

{-M(I0(u))p(x)u=λp(x)[λ1f(v)+μ1h(u)]in Ω,-M(I0(v))p(x)v=λp(x)[λ2g(u)+μ2τ(v)]in Ω,u=v=0on Ω,

where ΩN is a bounded smooth domain with C2 boundary Ω, p(x)u=div(|u|p(x)-2u), p(x)C1(Ω¯), with 1<p(x), is a function satisfying 1<p-=infΩp(x)p+=supΩp(x)<, λ, λ1, λ2, μ1 and μ2 are positive parameters, I0(u)=Ω1p(x)|u|p(x)𝑑x, and M(t) is a continuous function.

Acknowledgements

The authors would like to thank the anonymous referees and the handling editor for their careful reading and for relevant remarks/suggestions which helped to improve the paper. This presented work is in memory of the first author’s father Mr. Mahmoud ben Mouha Boulaaras (1910–1999).

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Received: 2017-06-16
Revised: 2017-12-12
Accepted: 2017-12-13
Published Online: 2018-01-18
Published in Print: 2019-01-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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