Open Access Research

Sub-super solutions for (p-q) Laplacian systems

Somayeh Haghaieghi1* and Ghasem Alizadeh Afrouzi2

Author Affiliations

1 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics, Faculty of Mathematical Sciences University of Mazandaran, Babolsar, Iran

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Boundary Value Problems 2011, 2011:52  doi:10.1186/1687-2770-2011-52

Published: 2 December 2011

Abstract

In this work, we consider the system:

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2011/1/52/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2011/1/52/mathml/M1">View MathML</a>

where Ω is a bounded region in RN with smooth boundary ∂Ω, Δp is the p-Laplacian operator defined by Δpu = div (|∇u|p-2u), p, q > 1 and g (x) is a C1 sign-changing the weight function, that maybe negative near the boundary. f, h, a, b are C1 non-decreasing functions satisfying a(0) ≥ 0, b(0) ≥ 0. Using the method of sub-super solutions, we prove the existence of weak solution.